33 research outputs found
A remark on the Castelnuovo-Mumford regularity of powers of ideal sheaves
We show that a bound of the Castelnuovo-Mumford regularity of any power of
the ideal sheaf of a smooth projective complex variety
is sharp exactly for complete intersections, provided the variety is cut
out scheme-theoretically by several hypersurfaces in . This
generalizes a result of Bertram-Ein-Lazarsfeld.Comment: 7 pages, to appear in the Journal of Pure and Applied Algebr
Well-posedness of stochastic partial differential equations with fully local monotone coefficients
Consider stochastic partial differential equations (SPDEs) with fully local
monotone coefficients in a Gelfand triple :
\begin{align*} \left\{ \begin{aligned}
dX(t) & = A(t,X(t))dt + B(t,X(t))dW(t), \quad t\in (0,T], \\
X(0) & = x\in H, \end{aligned} \right. \end{align*} where \begin{align*}
A: [0,T]\times V \rightarrow V^* , \quad B: [0,T]\times V \rightarrow
L_2(U,H) \end{align*} are measurable maps, is the space of
Hilbert-Schmidt operators from to and is a -cylindrical Wiener
process. Such SPDEs include many interesting models in applied fields like
fluid dynamics etc. In this paper, we establish the well-posedness of the above
SPDEs under fully local monotonicity condition solving a longstanding open
problem. The conditions on the diffusion coefficient are allowed
to depend on both the -norm and -norm. In the case of classical SPDEs,
this means that could also depend on the gradient of the
solution. The well-posedness is obtained through a combination of
pseudo-monotonicity techniques and compactness arguments.Comment: 45 page
Hard Lefschetz theorems for free line bundles
We introduce a partial positivity notion for algebraic maps via the defect of
semismallness. This positivity notion is modeled on -positivity in the
analytic setting and -ampleness in the geometric setting. Using this
positivity condition for algebraic maps, we establish K\"ahler packages, that
is, Hard Lefschetz theorems and Hodge-Riemann bilinear relations, for the
complete intersections of Chern classes of free line bundles.Comment: 14 pages; comments welcome
ChatRadio-Valuer: A Chat Large Language Model for Generalizable Radiology Report Generation Based on Multi-institution and Multi-system Data
Radiology report generation, as a key step in medical image analysis, is
critical to the quantitative analysis of clinically informed decision-making
levels. However, complex and diverse radiology reports with cross-source
heterogeneity pose a huge generalizability challenge to the current methods
under massive data volume, mainly because the style and normativity of
radiology reports are obviously distinctive among institutions, body regions
inspected and radiologists. Recently, the advent of large language models (LLM)
offers great potential for recognizing signs of health conditions. To resolve
the above problem, we collaborate with the Second Xiangya Hospital in China and
propose ChatRadio-Valuer based on the LLM, a tailored model for automatic
radiology report generation that learns generalizable representations and
provides a basis pattern for model adaptation in sophisticated analysts' cases.
Specifically, ChatRadio-Valuer is trained based on the radiology reports from a
single institution by means of supervised fine-tuning, and then adapted to
disease diagnosis tasks for human multi-system evaluation (i.e., chest,
abdomen, muscle-skeleton, head, and maxillofacial neck) from six different
institutions in clinical-level events. The clinical dataset utilized in this
study encompasses a remarkable total of \textbf{332,673} observations. From the
comprehensive results on engineering indicators, clinical efficacy and
deployment cost metrics, it can be shown that ChatRadio-Valuer consistently
outperforms state-of-the-art models, especially ChatGPT (GPT-3.5-Turbo) and
GPT-4 et al., in terms of the diseases diagnosis from radiology reports.
ChatRadio-Valuer provides an effective avenue to boost model generalization
performance and alleviate the annotation workload of experts to enable the
promotion of clinical AI applications in radiology reports