Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators

Uncertainty quantification (UQ) in scientific machine learning (SciML) becomes increasingly critical as neural networks (NNs) are being widely adopted in addressing complex problems across various scientific disciplines. Representative SciML models are physics-informed neural networks (PINNs) and neural operators (NOs). While UQ in SciML has been increasingly investigated in recent years, very few works have focused on addressing the uncertainty caused by the noisy inputs, such as spatial-temporal coordinates in PINNs and input functions in NOs. The presence of noise in the inputs of the models can pose significantly more challenges compared to noise in the outputs of the models, primarily due to the inherent nonlinearity of most SciML algorithms. As a result, UQ for noisy inputs becomes a crucial factor for reliable and trustworthy deployment of these models in applications involving physical knowledge. To this end, we introduce a Bayesian approach to quantify uncertainty arising from noisy inputs-outputs in PINNs and NOs. We show that this approach can be seamlessly integrated into PINNs and NOs, when they are employed to encode the physical information. PINNs incorporate physics by including physics-informed terms via automatic differentiation, either in the loss function or the likelihood, and often take as input the spatial-temporal coordinate. Therefore, the present method equips PINNs with the capability to address problems where the observed coordinate is subject to noise. On the other hand, pretrained NOs are also commonly employed as equation-free surrogates in solving differential equations and Bayesian inverse problems, in which they take functions as inputs. The proposed approach enables them to handle noisy measurements for both input and output functions with UQ

Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning

We address two major challenges in scientific machine learning (SciML): interpretability and computational efficiency. We increase the interpretability of certain learning processes by establishing a new theoretical connection between optimization problems arising from SciML and a generalized Hopf formula, which represents the viscosity solution to a Hamilton-Jacobi partial differential equation (HJ PDE) with time-dependent Hamiltonian. Namely, we show that when we solve certain regularized learning problems with integral-type losses, we actually solve an optimal control problem and its associated HJ PDE with time-dependent Hamiltonian. This connection allows us to reinterpret incremental updates to learned models as the evolution of an associated HJ PDE and optimal control problem in time, where all of the previous information is intrinsically encoded in the solution to the HJ PDE. As a result, existing HJ PDE solvers and optimal control algorithms can be reused to design new efficient training approaches for SciML that naturally coincide with the continual learning framework, while avoiding catastrophic forgetting. As a first exploration of this connection, we consider the special case of linear regression and leverage our connection to develop a new Riccati-based methodology for solving these learning problems that is amenable to continual learning applications. We also provide some corresponding numerical examples that demonstrate the potential computational and memory advantages our Riccati-based approach can provide

The Bone-Forming Effects of HIF-1α-Transduced BMSCs Promote Osseointegration with Dental Implant in Canine Mandible

The presence of insufficient bone volume remains a major clinical problem for dental implant placement to restore the oral function. Gene-transduced stem cells provide a promising approach for inducing bone regeneration and enhancing osseointegration in dental implants with tissue engineering technology. Our previous studies have demonstrated that the hypoxia-inducible factor-1α (HIF-1α) promotes osteogenesis in rat bone mesenchymal stem cells (BMSCs). In this study, the function of HIF-1α was validated for the first time in a preclinical large animal canine model in term of its ability to promote new bone formation in defects around implants as well as the osseointegration between tissue-engineered bone and dental implants. A lentiviral vector was constructed with the constitutively active form of HIF-1α (cHIF). The ectopic bone formation was evaluated in nude mice. The therapeutic potential of HIF-1α-overexpressing canine BMSCs in bone repair was evaluated in mesi-implant defects of immediate post-extraction implants in the canine mandible. HIF-1α mediated canine BMSCs significantly promoted new bone formation both subcutaneously and in mesi-implant defects, including increased bone volume, bone mineral density, trabecular thickness, and trabecular bone volume fraction. Furthermore, osseointegration was significantly enhanced by HIF-1α-overexpressing canine BMSCs. This study provides an important experimental evidence in a preclinical large animal model concerning to the potential applications of HIF-1α in promoting new bone formation as well as the osseointegration of immediate implantation for oral function restoration

Maspin expression in gastrointestinal stromal tumors

<p>Abstract</p> <p>Background</p> <p>To investigate the role of maspin expression in the progression of gastrointestinal stromal tumors, and its value as a prognostic indicator.</p> <p>Methods</p> <p>In the study 54 patients with GIST diagnosis were included in Uludag University of Faculty of Medicine, Department of Pathology between 1997-2007. The expression of maspin in 54 cases of gastrointestinal stromal tumor was detected by immunohistochemistry and compared with the clinicopathologic tumor parameters.</p> <p>Results</p> <p>The positive expression rates for maspin in the GISTs were 66,6% (36 of 54 cases). Maspin overexpression was detected in 9 of 29 high risk tumors (31%) and was significantly higher in very low/low (78.6%) and intermediate-risk tumors (63.6%) than high-risk tumors.</p> <p>Conclusions</p> <p>Maspin expression might be an important factor in tumor progression and patient prognosis in GIST. In the future, larger series may be studied to examine the prognostic significance of maspin in GISTs and, of course, maspin expression may be studied in different mesenchymal tumors.</p

Towards the clinical implementation of pharmacogenetics in bipolar disorder.

BackgroundBipolar disorder (BD) is a psychiatric illness defined by pathological alterations between the mood states of mania and depression, causing disability, imposing healthcare costs and elevating the risk of suicide. Although effective treatments for BD exist, variability in outcomes leads to a large number of treatment failures, typically followed by a trial and error process of medication switches that can take years. Pharmacogenetic testing (PGT), by tailoring drug choice to an individual, may personalize and expedite treatment so as to identify more rapidly medications well suited to individual BD patients.DiscussionA number of associations have been made in BD between medication response phenotypes and specific genetic markers. However, to date clinical adoption of PGT has been limited, often citing questions that must be answered before it can be widely utilized. These include: What are the requirements of supporting evidence? How large is a clinically relevant effect? What degree of specificity and sensitivity are required? Does a given marker influence decision making and have clinical utility? In many cases, the answers to these questions remain unknown, and ultimately, the question of whether PGT is valid and useful must be determined empirically. Towards this aim, we have reviewed the literature and selected drug-genotype associations with the strongest evidence for utility in BD.SummaryBased upon these findings, we propose a preliminary panel for use in PGT, and a method by which the results of a PGT panel can be integrated for clinical interpretation. Finally, we argue that based on the sufficiency of accumulated evidence, PGT implementation studies are now warranted. We propose and discuss the design for a randomized clinical trial to test the use of PGT in the treatment of BD

Measurement of the t(t)over-bar production cross section in the dilepton channel in pp collisions at √s=8 TeV

The top-antitop quark (t (t) over bar) production cross section is measured in proton-proton collisions at root s = 8 TeV with the CMS experiment at the LHC, using a data sample corresponding to an integrated luminosity of 5.3 fb(-1). The measurement is performed by analysing events with a pair of electrons or muons, or one electron and one muon, and at least two jets, one of which is identified as originating from hadronisation of a bottom quark. The measured cross section is 239 +/- 2 (stat.) +/- 11 (syst.) +/- 6 (lum.) pb, for an assumed top-quark mass of 172.5 GeV, in agreement with the prediction of the standard model

Post hoc pattern matching: assigning significance to statistically defined expression patterns in single channel microarray data

<p>Abstract</p> <p>Background</p> <p>Researchers using RNA expression microarrays in experimental designs with more than two treatment groups often identify statistically significant genes with ANOVA approaches. However, the ANOVA test does not discriminate which of the multiple treatment groups differ from one another. Thus, <it>post hoc </it>tests, such as linear contrasts, template correlations, and pairwise comparisons are used. Linear contrasts and template correlations work extremely well, especially when the researcher has <it>a priori </it>information pointing to a particular pattern/template among the different treatment groups. Further, all pairwise comparisons can be used to identify particular, treatment group-dependent patterns of gene expression. However, these approaches are biased by the researcher's assumptions, and some treatment-based patterns may fail to be detected using these approaches. Finally, different patterns may have different probabilities of occurring by chance, importantly influencing researchers' conclusions about a pattern and its constituent genes.</p> <p>Results</p> <p>We developed a four step, <it>post hoc </it>pattern matching (PPM) algorithm to automate single channel gene expression pattern identification/significance. First, 1-Way Analysis of Variance (ANOVA), coupled with <it>post hoc </it>'all pairwise' comparisons are calculated for all genes. Second, for each ANOVA-significant gene, all pairwise contrast results are encoded to create unique pattern ID numbers. The # genes found in each pattern in the data is identified as that pattern's 'actual' frequency. Third, using Monte Carlo simulations, those patterns' frequencies are estimated in random data ('random' gene pattern frequency). Fourth, a Z-score for overrepresentation of the pattern is calculated ('actual' against 'random' gene pattern frequencies). We wrote a Visual Basic program (StatiGen) that automates PPM procedure, constructs an Excel workbook with standardized graphs of overrepresented patterns, and lists of the genes comprising each pattern. The visual basic code, installation files for StatiGen, and sample data are available as supplementary material.</p> <p>Conclusion</p> <p>The PPM procedure is designed to augment current microarray analysis procedures by allowing researchers to incorporate all of the information from post hoc tests to establish unique, overarching gene expression patterns in which there is no overlap in gene membership. In our hands, PPM works well for studies using from three to six treatment groups in which the researcher is interested in treatment-related patterns of gene expression. Hardware/software limitations and extreme number of theoretical expression patterns limit utility for larger numbers of treatment groups. Applied to a published microarray experiment, the StatiGen program successfully flagged patterns that had been manually assigned in prior work, and further identified other gene expression patterns that may be of interest. Thus, over a moderate range of treatment groups, PPM appears to work well. It allows researchers to assign statistical probabilities to patterns of gene expression that fit <it>a priori </it>expectations/hypotheses, it preserves the data's ability to show the researcher interesting, yet unanticipated gene expression patterns, and assigns the majority of ANOVA-significant genes to non-overlapping patterns.</p

Fructose-Bisphophate Aldolase Exhibits Functional Roles between Carbon Metabolism and the hrp System in Rice Pathogen Xanthomonas oryzae pv. oryzicola

Fructose-bisphophate aldolase (FbaB), is an enzyme in glycolysis and gluconeogenesis in living organisms. The mutagenesis in a unique fbaB gene of Xanthomonas oryzae pv. oryzicola, the causal agent of rice bacterial leaf streak, led the pathogen not only unable to use pyruvate and malate for growth and delayed its growth when fructose was used as the sole carbon source, but also reduced extracellular polysaccharide (EPS) production and impaired bacterial virulence and growth in rice. Intriguingly, the fbaB promoter contains an imperfect PIP-box (plant-inducible promoter) (TTCGT-N9-TTCGT). The expression of fbaB was negatively regulated by a key hrp regulatory HrpG and HrpX cascade. Base substitution in the PIP-box altered the regulation of fbaB with the cascade. Furthermore, the expression of fbaB in X. oryzae pv. oryzicola RS105 strain was inducible in planta rather than in a nutrient-rich medium. Except other hrp-hrc-hpa genes, the expression of hrpG and hrpX was repressed and the transcripts of hrcC, hrpE and hpa3 were enhanced when fbaB was deleted. The mutation in hrcC, hrpE or hpa3 reduced the ability of the pathogen to acquire pyruvate and malate. In addition, bacterial virulence and growth in planta and EPS production in RΔfbaB mutant were completely restored to the wild-type level by the presence of fbaB in trans. This is the first report to demonstrate that carbohydrates, assimilated by X. oryzae pv. oryzicola, play critical roles in coordinating hrp gene expression through a yet unknown regulator

A rapid high-performance semi-automated tool to measure total kidney volume from MRI in autosomal dominant polycystic kidney disease.

OBJECTIVES: To develop a high-performance, rapid semi-automated method (Sheffield TKV Tool) for measuring total kidney volume (TKV) from magnetic resonance images (MRI) in patients with autosomal dominant polycystic kidney disease (ADPKD). METHODS: TKV was initially measured in 61 patients with ADPKD using the Sheffield TKV Tool and its performance compared to manual segmentation and other published methods (ellipsoidal, mid-slice, MIROS). It was then validated using an external dataset of MRI scans from 65 patients with ADPKD. RESULTS: Sixty-one patients (mean age 45 ± 14 years, baseline eGFR 76 ± 32 ml/min/1.73 m2) with ADPKD had a wide range of TKV (258-3680 ml) measured manually. The Sheffield TKV Tool was highly accurate (mean volume error 0.5 ± 5.3% for right kidney, - 0.7 ± 5.5% for left kidney), reproducible (intra-operator variability - 0.2 ± 1.3%; inter-operator variability 1.1 ± 2.9%) and outperformed published methods. It took less than 6 min to execute and performed consistently with high accuracy in an external MRI dataset of T2-weighted sequences with TKV acquired using three different scanners and measured using a different segmentation methodology (mean volume error was 3.45 ± 3.96%, n = 65). CONCLUSIONS: The Sheffield TKV Tool is operator friendly, requiring minimal user interaction to rapidly, accurately and reproducibly measure TKV in this, the largest reported unselected European patient cohort with ADPKD. It is more accurate than estimating equations and its accuracy is maintained at larger kidney volumes than previously reported with other semi-automated methods. It is free to use, can run as an independent executable and will accelerate the application of TKV as a prognostic biomarker for ADPKD into clinical practice. KEY POINTS: • This new semi-automated method (Sheffield TKV Tool) to measure total kidney volume (TKV) will facilitate the routine clinical assessment of patients with ADPKD. • Measuring TKV manually is time consuming and laborious. • TKV is a prognostic indicator in ADPKD and the only imaging biomarker approved by the FDA and EMA

Systematic Analysis of Pleiotropy in C. elegans Early Embryogenesis

Pleiotropy refers to the phenomenon in which a single gene controls several distinct, and seemingly unrelated, phenotypic effects. We use C. elegans early embryogenesis as a model to conduct systematic studies of pleiotropy. We analyze high-throughput RNA interference (RNAi) data from C. elegans and identify “phenotypic signatures”, which are sets of cellular defects indicative of certain biological functions. By matching phenotypic profiles to our identified signatures, we assign genes with complex phenotypic profiles to multiple functional classes. Overall, we observe that pleiotropy occurs extensively among genes involved in early embryogenesis, and a small proportion of these genes are highly pleiotropic. We hypothesize that genes involved in early embryogenesis are organized into partially overlapping functional modules, and that pleiotropic genes represent “connectors” between these modules. In support of this hypothesis, we find that highly pleiotropic genes tend to reside in central positions in protein-protein interaction networks, suggesting that pleiotropic genes act as connecting points between different protein complexes or pathways