Products and Commutators of Martingales in H1H_1 and BMO{\rm BMO}

Let $f:=(f_n)_{n\in \mathbb{Z}_+}$ and $g:=(g_n)_{n\in \mathbb{Z}_+}$ be two martingales related to the probability space $(\Omega,\mathcal F,\mathbb P)$ equipped with the filtration $(\mathcal F_n)_{n\in \mathbb{Z}_+}.$ Assume that $f$ is in the martingale Hardy space $H_1$ and $g$ is in its dual space, namely the martingale $\rm BMO.$ Then the semi-martingale $f\cdot g:=(f_ng_n)_{n\in \mathbb{Z}_+}$ may be written as the sum $$f\cdot g=G(f, g)+L( f,g).$$ Here $L( f,g):=(L( f,g)_n)_{n\in\mathbb{Z}_+}$ with $L( f,g)_n:=\sum_{k=0}^n(f_k-f_{k-1})(g_k-g_{k-1)})$ for any $n\in\mathbb{Z}_+$, where $f_{-1}:=0=:g_{-1}$. The authors prove that $L( f,g)$ is a process with bounded variation and limit in $L^1,$ while $G(f,g)$ belongs to the martingale Hardy-Orlicz space $H_{\log}$ associated with the Orlicz function $$\Phi(t):=\frac{t}{\log(e+t)},\quad \forall\, t\in[0,\infty).$$ The above bilinear decomposition $L^1+H_{\log}$ is sharp in the sense that, for particular martingales, the space $L^1+H_{\log}$ cannot be replaced by a smaller space having a larger dual. As an application, the authors characterize the largest subspace of $H_1$, denoted by $H^b_1$ with $b\in {\rm BMO}$, such that the commutators $[T, b]$ with classical sublinear operators $T$ are bounded from $H^b_1$ to $L^1$. This endpoint boundedness of commutators allow the authors to give more applications. On the one hand, in the martingale setting, the authors obtain the endpoint estimates of commutators for both martingale transforms and martingale fractional integrals. On the other hand, in harmonic analysis, the authors establish the endpoint estimates of commutators both for the dyadic Hilbert transform beyond doubling measures and for the maximal operator of Ces\`{a}ro means of Walsh--Fourier series.Comment: 42 pages, Submitte

A New Manufacturing Service Selection and Composition Method Using Improved Flower Pollination Algorithm

With an increasing number of manufacturing services, the means by which to select and compose these manufacturing services have become a challenging problem. It can be regarded as a multiobjective optimization problem that involves a variety of conflicting quality of service (QoS) attributes. In this study, a multiobjective optimization model of manufacturing service composition is presented that is based on QoS and an environmental index. Next, the skyline operator is applied to reduce the solution space. And then a new method called improved Flower Pollination Algorithm (FPA) is proposed for solving the problem of manufacturing service selection and composition. The improved FPA enhances the performance of basic FPA by combining the latter with crossover and mutation operators of the Differential Evolution (DE) algorithm. Finally, a case study is conducted to compare the proposed method with other evolutionary algorithms, including the Genetic Algorithm, DE, basic FPA, and extended FPA. The experimental results reveal that the proposed method performs best at solving the problem of manufacturing service selection and composition

Molecular Bubble and Outflow in S Mon Revealed by Multiband Datasets

We identify a molecular bubble, and study the star formation and its feedback in the S Mon region, using multiple molecular lines, young stellar objects (YSOs), and infrared data. We revisit the distance to S Mon, ~722+/-9 pc, using Gaia Data Release 3 parallaxes of the associated Class II YSOs. The bubble may be mainly driven by a massive binary system (namely 15 Mon), the primary of which is an O7V-type star. An outflow is detected in the shell of the bubble, suggesting ongoing star formation activities in the vicinity of the bubble. The total wind energy of the massive binary star is three orders of magnitude higher than the sum of the observed turbulent energy in the molecular gas and the kinetic energy of the bubble, indicating that stellar winds help to maintain the turbulence in the S Mon region and drive the bubble. We conclude that the stellar winds of massive stars have an impact on their surrounding environment.Comment: 34 pages,19 figures, 5 tables, Accepted for publication in Ap

Distributions and Physical Properties of Molecular Clouds in the Third Galactic Quadrant: ll = [219.75, 229.75]∘^\circ and bb = [-5.25, 5.25]∘^\circ

We present the results of an unbiased $^{12}$CO/$^{13}$CO/C$^{18}$O ($J$ = 1-0) survey in a portion of the third Galactic quadrant (TGQ): $l$ = [219.75, 229.75]$^\circ$ and $b$ = [-5.25, 5.25]$^\circ$. The high-resolution and high-sensitivity data sets help to unravel the distributions and physical properties of the molecular clouds (MCs) in the mapped area. In the LSR velocity range from -1 to 85 km/s, the molecular material successfully traces the Local, Perseus, and Outer arms. In the TGQ, the Outer arm appears to be more prominent than that in the second Galactic quadrant (SGQ), but the Perseus arm is not as conspicuous as that in the SGQ. A total of 1,502 $^{12}$CO, 570 $^{13}$CO, and 53 C$^{18}$O molecular structures are identified, spanning over $\sim2$ and $\sim6$ orders of magnitude in size and mass, respectively. Tight mass-radius correlations and virial parameter-mass anticorrelations are observable. Yet, it seems that no clear correlations between velocity dispersion and effective radius can be found over the full dynamic range. The vertical distribution of the MCs renders evident pictures of the Galactic warp and flare.Comment: 22 pages, 13 figures, 7 tables (with machine-readable versions), published in ApJ

DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence

The rapid development of large language models has revolutionized code intelligence in software development. However, the predominance of closed-source models has restricted extensive research and development. To address this, we introduce the DeepSeek-Coder series, a range of open-source code models with sizes from 1.3B to 33B, trained from scratch on 2 trillion tokens. These models are pre-trained on a high-quality project-level code corpus and employ a fill-in-the-blank task with a 16K window to enhance code generation and infilling. Our extensive evaluations demonstrate that DeepSeek-Coder not only achieves state-of-the-art performance among open-source code models across multiple benchmarks but also surpasses existing closed-source models like Codex and GPT-3.5. Furthermore, DeepSeek-Coder models are under a permissive license that allows for both research and unrestricted commercial use

Optimal Waveforms Design for Ultra-Wideband Impulse Radio Sensors

Ultra-wideband impulse radio (UWB-IR) sensors should comply entirely with the regulatory spectral limits for elegant coexistence. Under this premise, it is desirable for UWB pulses to improve frequency utilization to guarantee the transmission reliability. Meanwhile, orthogonal waveform division multiple-access (WDMA) is significant to mitigate mutual interferences in UWB sensor networks. Motivated by the considerations, we suggest in this paper a low complexity pulse forming technique, and its efficient implementation on DSP is investigated. The UWB pulse is derived preliminarily with the objective of minimizing the mean square error (MSE) between designed power spectrum density (PSD) and the emission mask. Subsequently, this pulse is iteratively modified until its PSD completely conforms to spectral constraints. The orthogonal restriction is then analyzed and different algorithms have been presented. Simulation demonstrates that our technique can produce UWB waveforms with frequency utilization far surpassing the other existing signals under arbitrary spectral mask conditions. Compared to other orthogonality design schemes, the designed pulses can maintain mutual orthogonality without any penalty on frequency utilization, and hence, are much superior in a WDMA network, especially with synchronization deviations

Allogeneic Mesenchymal Cell Therapy in Anthracycline-Induced Cardiomyopathy Heart Failure Patients: The CCTRN SENECA Trial.

BACKGROUND: Anthracycline-induced cardiomyopathy (AIC) may be irreversible with a poor prognosis, disproportionately affecting women and young adults. Administration of allogeneic bone marrow-derived mesenchymal stromal cells (allo-MSCs) is a promising approach to heart failure (HF) treatment. OBJECTIVES: SENECA (Stem Cell Injection in Cancer Survivors) was a phase 1 study of allo-MSCs in AIC. METHODS: Cancer survivors with chronic AIC (mean age 56.6 years; 68% women; NT-proBNP 1,426 pg/ml; 6 enrolled in an open-label, lead-in phase and 31 subjects randomized 1:1) received 1 × 10 RESULTS: A total of 97% of subjects underwent successful study product injections; all allo-MSC-assigned subjects received the target dose of cells. Follow-up visits were well-attended (92%) with successful collection of endpoints in 94% at the 1-year visit. Although 58% of subjects had non-CMR compatible devices, CMR endpoints were successfully collected in 84% of subjects imaged at 1 year. No new tumors were reported. There were no significant differences between allo-MSC and vehicle groups with regard to clinical outcomes. Secondary measures included 6-min walk test (p = 0.056) and Minnesota Living with Heart Failure Questionnaire score (p = 0.048), which tended to favor the allo-MSC group. CONCLUSIONS: In this first-in-human study of cell therapy in patients with AIC, transendocardial administration of allo-MSCs appears safe and feasible, and CMR was successfully performed in the majority of the HF patients with devices. This study lays the groundwork for phase 2 trials aimed at assessing efficacy of cell therapy in patients with AIC

DeepSeek LLM: Scaling Open-Source Language Models with Longtermism

The rapid development of open-source large language models (LLMs) has been truly remarkable. However, the scaling law described in previous literature presents varying conclusions, which casts a dark cloud over scaling LLMs. We delve into the study of scaling laws and present our distinctive findings that facilitate scaling of large scale models in two commonly used open-source configurations, 7B and 67B. Guided by the scaling laws, we introduce DeepSeek LLM, a project dedicated to advancing open-source language models with a long-term perspective. To support the pre-training phase, we have developed a dataset that currently consists of 2 trillion tokens and is continuously expanding. We further conduct supervised fine-tuning (SFT) and Direct Preference Optimization (DPO) on DeepSeek LLM Base models, resulting in the creation of DeepSeek Chat models. Our evaluation results demonstrate that DeepSeek LLM 67B surpasses LLaMA-2 70B on various benchmarks, particularly in the domains of code, mathematics, and reasoning. Furthermore, open-ended evaluations reveal that DeepSeek LLM 67B Chat exhibits superior performance compared to GPT-3.5