This paper considers optimization problems on the Stiefel manifold
X
T
X
=
I
p
, where
X
∈
R
n
×
p
is the variable and
I
p
is the
p
-by-
p
identity matrix. A framework of constraint preserving update ...schemes is proposed by decomposing each feasible point into the range space of
X
and the null space of
X
T
. While this general framework can unify many existing schemes, a new update scheme with low complexity cost is also discovered. Then we study a feasible Barzilai–Borwein-like method under the new update scheme. The global convergence of the method is established with an adaptive nonmonotone line search. The numerical tests on the nearest low-rank correlation matrix problem, the Kohn–Sham total energy minimization and a specific problem from statistics demonstrate the efficiency of the new method. In particular, the new method performs remarkably well for the nearest low-rank correlation matrix problem in terms of speed and solution quality and is considerably competitive with the widely used SCF iteration for the Kohn–Sham total energy minimization.
LINKED CONTENT
This article is linked to Marasco et al papers. To view these articles, visit https://doi.org/10.1111/apt.17513 and https://doi.org/10.1111/apt.17554
ObjectiveThe SARS-CoV-2-infected disease (COVID-19) outbreak is a major threat to human beings. Previous studies mainly focused on Wuhan and typical symptoms. We analysed 74 confirmed COVID-19 cases ...with GI symptoms in the Zhejiang province to determine epidemiological, clinical and virological characteristics.DesignCOVID-19 hospital patients were admitted in the Zhejiang province from 17 January 2020 to 8 February 2020. Epidemiological, demographic, clinical, laboratory, management and outcome data of patients with GI symptoms were analysed using multivariate analysis for risk of severe/critical type. Bioinformatics were used to analyse features of SARS-CoV-2 from Zhejiang province.ResultsAmong enrolled 651 patients, 74 (11.4%) presented with at least one GI symptom (nausea, vomiting or diarrhoea), average age of 46.14 years, 4-day incubation period and 10.8% had pre-existing liver disease. Of patients with COVID-19 with GI symptoms, 17 (22.97%) and 23 (31.08%) had severe/critical types and family clustering, respectively, significantly higher than those without GI symptoms, 47 (8.14%) and 118 (20.45%). Of patients with COVID-19 with GI symptoms, 29 (39.19%), 23 (31.08%), 8 (10.81%) and 16 (21.62%) had significantly higher rates of fever >38.5°C, fatigue, shortness of breath and headache, respectively. Low-dose glucocorticoids and antibiotics were administered to 14.86% and 41.89% of patients, respectively. Sputum production and increased lactate dehydrogenase/glucose levels were risk factors for severe/critical type. Bioinformatics showed sequence mutation of SARS-CoV-2 with m6A methylation and changed binding capacity with ACE2.ConclusionWe report COVID-19 cases with GI symptoms with novel features outside Wuhan. Attention to patients with COVID-19 with non-classic symptoms should increase to protect health providers.
Anionic redox activity can trigger structural instability in Li‐rich Mn‐based cathodes. Lattice oxygen activity can be tuned through liquid acid‐induced spinel phases and oxygen vacancies. However, ...the liquid‐acid‐modified surface is still attacked by the electrolyte. Besides, the underlying mechanism of spinel phase suppression of lattice oxygen activity is controversial. Here, a solid acid strategy for modification is proposed and the underlying mechanism is investigated in detail. Unique solid acid can in situ generate an interface protection layer and remarkably stabilize the structure. Theoretical calculations and experimental characterizations reveal that the spinel phase suppresses the irreversible loss of lattice oxygen by decreasing the O 2p non‐bonding energy level and enriching electrons at the layered/spinel phase interface. The inert layer on the surface prevents highly active On− from being attacked by electrolytes. The obtained material exhibits significantly reduced irreversible lattice oxygen release and improved electrochemical performance. After 300 cycles, a slow capacity fading of 0.177 mAh g−1 per cycle and suppressed voltage fading are achieved. This study reveals the regulation method and mechanism for the anion activity of oxide cathodes in next‐generation Li‐ion batteries.
The lattice oxygen activity of Li‐rich Mn‐based cathode materials is well regulated by solid acid modification. The O 2p non‐bonding band is lowered and electrons are enriched at the layered/spinel interface, which effectively suppresses the irreversible release of lattice oxygen. The modified material with a stable reversible structure shows suppressed O2 release and enhances electrochemical performance.
Training generative adversarial networks (GANs) often suffers from cyclic behaviours of iterates. Based on a simple intuition that the direction of centripetal acceleration of an object moving in ...uniform circular motion is toward the centre of the circle, we present the Simultaneous Centripetal Acceleration (SCA) method and the Alternating Centripetal Acceleration (ACA) method to alleviate the cyclic behaviours. Under suitable conditions, gradient descent methods with either SCA or ACA are shown to be linearly convergent for bilinear games. Numerical experiments are conducted by applying ACA to existing gradient-based algorithms in a GAN setup scenario, which demonstrate the superiority of ACA.
Consider a multi-user orthogonal frequency division multiple access (OFDMA) system where multiple users share multiple discrete subcarriers, but at most one user is allowed to transmit power on each ...subcarrier. To adapt fast traffic and channel fluctuations and improve the spectrum efficiency, the system should have the ability to dynamically allocate subcarriers and power resources to users. Assuming perfect channel knowledge, two formulations for the joint subcarrier and power allocation problem are considered in this paper: the first is to minimize the total transmission power subject to the quality of service constraints and the OFDMA constraint, and the second is to maximize some system utility function subject to the total transmission power constraint per user and the OFDMA constraint. In spite of the existence of various heuristics approaches, little is known about the computational complexity status of the above problem. This paper aims at filling this theoretical gap, i.e., characterizing the complexity of the joint subcarrier and power allocation problem for the multi-user OFDMA system. It is shown in this paper that both formulations of the joint subcarrier and power allocation problem are strongly NP-hard. Several subclasses of the problem which can be solved efficiently in polynomial time are also identified. These complexity results suggest that there are not polynomial time algorithms that are able to solve the general joint subcarrier and power allocation problem to global optimality (unless P=NP), and determining an approximately optimal subcarrier and power allocation strategy is more realistic in practice.
There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation ...prefer to be found. A natural way for dealing with these problems is to extend the nonlinear optimization problem as the one optimizing the objective function over the set of points with the least constraint violation. This leads to the study of the shifted problem. This paper focuses on the constrained convex optimization problem. The sufficient condition for the closedness of the set of feasible shifts is presented and the continuity properties of the optimal value function and the solution mapping for the shifted problem are studied. Properties of the conjugate dual of the shifted problem are discussed through the relations between the dual function and the optimal value function. The solvability of the dual of the optimization problem with the least constraint violation is investigated. It is shown that, if the least violated shift is in the domain of the subdifferential of the optimal value function, then this dual problem has an unbounded solution set. Under this condition, the optimality conditions for the problem with the least constraint violation are established in term of the augmented Lagrangian. It is shown that the augmented Lagrangian method has the properties that the sequence of shifts converges to the least violated shift and the sequence of multipliers is unbounded. Moreover, it is proved that the augmented Lagrangian method is able to find an approximate solution to the problem with the least constraint violation and it has linear rate of convergence under an error bound condition. The augmented Lagrangian method is applied to an illustrative convex second-order cone constrained optimization problem with least constraint violation and numerical results verify our theoretical results.
The best donor for a related donor for a human leukocyte antigen (HLA) haplotype-mismatched transplant for hematological neoplasms is controversial. We studied outcomes in 1210 consecutive transplant ...recipients treated on a uniform protocol. Younger donors and male donors were associated with less nonrelapse mortality (NRM; hazard ratio HR = 0.30; 95% confidence interval CI = 0.01-0.39; P = .008 and HR = 0.65; 95% CI = 0.49-0.85; P = .002) and better survival (HR = 0.73; 95% CI = 0.54-0.97; P = .033 and HR = 0.73; 95% CI = 0.59-0.91; P = .005). Father donors were associated with less NRM (HR = 0.65; 95% CI = 0.45-0.95; P = .02), acute graft-versus-host disease (GVHD) (HR = 0.69; 95% CI = 0.55-0.86; P = .001), and better survival (HR = 0.66; 95% CI = 0.50-0.87; P = .003) compared with mother donors. Children donors were associated with less acute GVHD than sibling donors (HR = 0.57; 95% CI = 0.31-0.91; P = .01). Older sister donors were inferior to father donors with regard to NRM (HR = 1.87; 95% CI = 1.10-3.20; P = .02) and survival (HR = 1.59; 95% CI = 1.05-2.40; P = .03). Noninherited maternal antigen-mismatched sibling donors were associated with the lowest incidence of acute GVHD compared with parental donors and noninherited paternal antigen-mismatched sibling donors. Specific HLA disparities were not significantly correlated with transplant outcomes. Our data indicate which HLA haplotype-mismatched related donors are associated with the best transplant outcomes in persons with hematological neoplasms.
•There is a need to identify the best HLA haplotype-mismatched related donor.•Use of young, male, NIMA-mismatched donors results in the best survival after HLA haplotype-mismatched related donor transplants.
In a cellular wireless system, users located at cell edges often suffer significant out-of-cell interference. Assuming each base station is equipped with multiple antennas, we can model this scenario ...as a multiple-input single-output (MISO) interference channel. In this paper we consider a coordinated beamforming approach whereby multiple base stations jointly optimize their downlink beamforming vectors in order to simultaneously improve the data rates of a given group of cell edge users. Assuming perfect channel knowledge, we formulate this problem as the maximization of a system utility (which balances user fairness and average user rates), subject to individual power constraints at each base station. We show that, for the single-carrier case and when the number of antennas at each base station is at least two, the optimal coordinated beamforming problem is NP-hard for both the harmonic mean utility and the proportional fairness utility. For general utilities, we propose a cyclic coordinate descent algorithm, which enables each transmitter to update its beamformer locally with limited information exchange and establish its global convergence to a stationary point. We illustrate its effectiveness in computer simulations by using the space matched beamformer as the benchmark.
Many patients who require allogeneic hematopoietic stem cell transplantation (allo-HSCT) lack a human leukocyte antigen (HLA)-matched donor. Recently, a new strategy was developed for ...HLA-mismatched/haploidentical transplantation from family donors without in vitro T cell depletion (TCD).
Over the past 9 years, 756 patients underwent haploidentical transplantation using a protocol developed by the authors, which combines granulocyte-colony stimulating factor-primed bone marrow (G-BM) and peripheral blood stem cells without in vitro TCD. The long-term outcome with this treatment modality was reported, and a risk-factor analysis was provided.
Of these patients, 752 (99%) achieved sustained, full donor chimerism. The incidence of grades 2 through 4 acute graft-versus-host disease (GVHD) was 43%, and the 2-year cumulative incidence of total chronic GVHD was 53%. The 3-year cumulative incidence of nonrelapse mortality was 18%. The 2-year cumulative incidences of relapse were 15% and 26% in the standard-risk and high-risk groups, respectively. Of the 756 patients, 480 survived throughout the follow-up period of 1154 days (range: 335-3511 days) with the 3-year leukemia-free survival rates of 68% and 49% in the standard-risk and high-risk groups, respectively. Lower leukemia-free survival was associated with high-risk disease status (P = .001), chronic myelogenous leukemia disease type (P = .004), neutrophil engraftment beyond 13 days after transplant (P = .012), and the occurrence of grades 2 through 4 acute GVHD (P = .019).
The results from the authors' 9-year experience showed that G-BM combined with peripheral blood stem cells from haploidentical donors, without in vitro TCD, is a reliable source of stem cells for transplantation by using the protocol developed by the authors.
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