An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem

The multiple-sets split equality problem (MSSEP) requires finding a point x∈∩i=1NCi, y∈∩j=1MQj such that Ax=By, where N and M are positive integers, {C1,C2,…,CN} and {Q1,Q2,…,QM} are closed convex subsets of Hilbert spaces H1, H2, respectively, and A:H1→H3, B:H2→H3 are two bounded linear operators. When N=M=1, the MSSEP is called the split equality problem (SEP). If  B=I, then the MSSEP and SEP reduce to the well-known multiple-sets split feasibility problem (MSSFP) and split feasibility problem (SFP), respectively. One of the purposes of this paper is to introduce an iterative algorithm to solve the SEP and MSSEP in the framework of infinite-dimensional Hilbert spaces under some more mild conditions for the iterative coefficient

Learning A Foundation Language Model for Geoscience Knowledge Understanding and Utilization

Large language models (LLMs)have achieved great success in general domains of natural language processing. In this paper, we bring LLMs to the realm of geoscience, with the objective of advancing research and applications in this field. To this end, we present the first-ever LLM in geoscience, K2, alongside a suite of resources developed to further promote LLM research within geoscience. For instance, we have curated the first geoscience instruction tuning dataset, GeoSignal, which aims to align LLM responses to geoscience-related user queries. Additionally, we have established the first geoscience benchmark, GeoBenchmark, to evaluate LLMs in the context of geoscience. In this work, we experiment with a complete recipe to adapt a pretrained general-domain LLM to the geoscience domain. Specifically, we further train the LLaMA-7B model on over 1 million pieces of geoscience literature and utilize GeoSignal's supervised data to fine-tune the model. Moreover, we share a protocol that can efficiently gather domain-specific data and construct domain-supervised data, even in situations where manpower is scarce. Experiments conducted on the GeoBenchmark demonstrate the the effectiveness of our approach and datasets

Inferring the Individual Psychopathologic Deficits With Structural Connectivity in a Longitudinal Cohort of Schizophrenia.

The prediction of schizophrenia-related psychopathologic deficits is exceedingly important in the fields of psychiatry and clinical practice. However, objective association of the brain structure alterations to the illness clinical symptoms is challenging. Although, schizophrenia has been characterized as a brain dysconnectivity syndrome, evidence accounting for neuroanatomical network alterations remain scarce. Moreover, the absence of generalized connectome biomarkers for the assessment of illness progression further perplexes the prediction of long-term symptom severity. In this paper, a combination of individualized prediction models with quantitative graph theoretical analysis was adopted, providing a comprehensive appreciation of the extent to which the brain network properties are affected over time in schizophrenia. Specifically, Connectome-based Prediction Models were employed on Structural Connectivity (SC) features, efficiently capturing individual network-related differences, while identifying the anatomical connectivity disturbances contributing to the prediction of psychopathological deficits. Our results demonstrated distinctions among widespread cortical circuits responsible for different domains of symptoms, indicating the complex neural mechanisms underlying schizophrenia. Furthermore, the generated models were able to significantly predict changes of symptoms using SC features at follow-up, while the preserved SC features suggested an association with improved positive and overall symptoms. Moreover, cross-sectional significant deficits were observed in network efficiency and a progressive aberration of global integration in patients compared to healthy controls, representing a group-consensus pathological map, while supporting the dysconnectivity hypothesis

Iterative algorithm for solving the multiple-sets split equality problem with split self-adaptive step size in Hilbert spaces

Abstract The split equality problem is a generalization of the split feasibility problem, meanwhile it is a special case of multiple-sets split equality problems. In this paper, we propose an iterative algorithm for solving the multiple-sets split equality problem whose iterative step size is split self-adaptive. The advantage of the split self-adaptive step size is that it could be obtained directly from the iterative procedure without needing to have any information of the spectral norm of the related operators. Under suitable conditions, we establish the theoretical convergence of the algorithm proposed in Hilbert spaces, and several numerical results confirm the effectiveness of the algorithm proposed

Convergence analysis of an iterative algorithm for the extended regularized nonconvex variational inequalities

Abstract In this paper, we suggest and analyze a new system of extended regularized nonconvex variational inequalities and prove the equivalence between the aforesaid system and a fixed point problem. We introduce a new perturbed projection iterative algorithm with mixed errors to find the solution of the system of extended regularized nonconvex variational inequalities. Furthermore, under moderate assumptions, we research the convergence analysis of the suggested iterative algorithm

Linear convergence of the relaxed gradient projection algorithm for solving the split equality problems in Hilbert spaces

Abstract In this paper, we consider the relaxed gradient projection algorithm to solve the split equality problem in Hilbert spaces, and we investigate its linear convergence. In particular, we use the concept of the bounded linear regularity property for the split equality problem to prove the linear convergence property for the above algorithm. Furthermore, we conclude the linear convergence rate of the relaxed gradient projection algorithm. Finally, some numerical experiments are given to test the validity of our results

Construction of Photoinitiator Functionalized Spherical Nanoparticles Enabling Favorable Photoinitiating Activity and Migration Resistance for 3D Printing

A straight-forward method was exploited to construct a multifunctional hybrid photoinitiator by supporting 2-hydroxy-2-methylpropiophenone (HMPP) onto a nano-silica surface through a chemical reaction between silica and HMPP by using (3-isocyanatopropyl)-triethoxysilane (IPTS) as a bridge, and this was noted as silica-s-HMPP. The novel hybrid-photoinitiator can not only initiate the photopolymerization but also prominently improve the dispersion of nanoparticles in the polyurethane acrylate matrix and enhance the filler-elastomer interfacial interaction, which results in excellent mechanical properties of UV-cured nanocomposites. Furthermore, the amount of extractable residual photoinitiators in the UV-cured system of silica-s-HPMM shows a significant decrease compared with the original HPMM system. Since endowing the silica nanoparticle with photo-initiated performance and fairly lower mobility, it may lead to a reduction in environmental contamination compared to traditional photoinitators. In addition, the hybrid-photoinitiator gives rise to an accurate resolution object with a complex construction and favorable surface morphology, indicating that multifunctional nanosilica particles can be applied in stereolithographic 3D printing

Neighborhood Matters: Influence Maximization in Social Networks with Limited Access

Influence maximization (IM) aims at maximizing the spread of influence by offering discounts to influential users (called seeding). In many applications, due to user's privacy concern, overwhelming network scale etc., it is hard to target any user in the network as one wishes. Instead, only a small subset of users is initially accessible. Such access limitation would significantly impair the influence spread, since IM often relies on seeding high degree users, which are particularly rare in such a small subset due to the power-law structure of social networks. In this paper, we attempt to solve the limited IM in real-world scenarios by the adaptive approach with seeding and diffusion uncertainty considered. Specifically, we consider fine-grained discounts and assume users accept the discount probabilistically. The diffusion process is depicted by the independent cascade model. To overcome the access limitation, we prove the set-wise friendship paradox (FP) phenomenon that neighbors have higher degree in expectation, and propose a two-stage seeding model with the FP embedded, where neighbors are seeded. On this basis, for comparison we formulate the non-adaptive case and adaptive case, both proven to be NP-hard. In the non-adaptive case, discounts are allocated to users all at once. We show the monotonicity of influence spread w.r.t. discount allocation and design a two-stage coordinate descent framework to decide the discount allocation. In the adaptive case, users are sequentially seeded based on observations of existing seeding and diffusion results. We prove the adaptive submodularity and submodularity of the influence spread function in two stages. Then, a series of adaptive greedy algorithms are proposed with constant approximation ratio.Comment: Already accepted by IEEE Transactions on Knowledge and Data Engineering, 21 pages including 15 pages main paper and 6 pages supplemental fil