Neural ODEs and i-ResNet are recently proposed methods for enforcing invertibility of residual neural models. Having a generic technique for constructing invertible models can open new avenues for advances in learning systems, but so far the question of whether Neural ODEs and i-ResNets can model any continuous invertible function remained unresolved. Here, we show that both of these models are limited in their approximation capabilities. We then prove that any homeomorphism on a $p$-dimensional Euclidean space can be approximated by a Neural ODE operating on a $2p$-dimensional Euclidean space, and a similar result for i-ResNets. We conclude by showing that capping a Neural ODE or an i-ResNet with a single linear layer is sufficient to turn the model into a universal approximator for non-invertible continuous functions.
Many novel therapeutics originally aimed at a specific protein have in fact complex target profiles and interact promiscuously with many other proteins and pathways. Discovering new molecular targets and related pharmacodynamic effectors for existing drugs can help us understand mechanisms behind drug resistance, discover potential side effects, and point to target for new drugs. Often, the study of novel targets and receptors starts with building up diverse panel of drug sensitive and resistant cell lines, which is then profiled using high-throughput method such as gene expression microarrays or proteomic arrays. Analysis of profiling data requires statistical methods that move beyond univariate tests of differential expression between sensitive and resistant cell lines. Here, we propose a new approach for analysing differential co-expression, which allows for detecting changes of co-expression pattern in gene pairs, bringing spotlight on the differences in complex dynamic relationships and regulation mechanisms between genes in sensitive and resistant phenotypes. In contrast to existing methods, the proposed approach can deal with confounding factors such as tissue heterogeneity of the cell line panels that leads to presence of clusters and outliers, and together with relatively small number of samples can result in many false discoveries. We applied our method to study differences of gene co-expression patterns between cell lines sensitive and resistant to dasatinib, a novel targeted anticancer drug, and we discovered a closely-linked network of differentially co-expressed genes related to molecular effects of the drug.
The NCI-60 cell line set is likely the most molecularly profiled set of human tumor cell lines in the world. However, a critical missing component of previous analyses has been the inability to place the massive amounts of "-omic" data in the context of functional protein signaling networks, which often contain many of the drug targets for new targeted therapeutics. We used reverse-phase protein array (RPPA) analysis to measure the activation/phosphorylation state of 135 proteins, with a total analysis of nearly 200 key protein isoforms involved in cell proliferation, survival, migration, adhesion, etc., in all 60 cell lines. We aggregated the signaling data into biochemical modules of interconnected kinase substrates for 6 key cancer signaling pathways: AKT, mTOR, EGF receptor (EGFR), insulin-like growth factor-1 receptor (IGF-1R), integrin, and apoptosis signaling. The net activation state of these protein network modules was correlated to available individual protein, phosphoprotein, mutational, metabolomic, miRNA, transcriptional, and drug sensitivity data. Pathway activation mapping identified reproducible and distinct signaling cohorts that transcended organ-type distinctions. Direct correlations with the protein network modules involved largely protein phosphorylation data but we also identified direct correlations of signaling networks with metabolites, miRNA, and DNA data. The integration of protein activation measurements into biochemically interconnected modules provided a novel means to align the functional protein architecture with multiple "-omic" data sets and therapeutic response correlations. This approach may provide a deeper understanding of how cellular biochemistry defines therapeutic response. Such "-omic" portraits could inform rational anticancer agent screenings and drive personalized therapeutic approaches.
Wetting-induced soil deformation significantly impacts land stability and management on the Chinese Loess Plateau. This study analyzed silt soils from the Late Pleistocene (1 m depth) and Middle Pleistocene (25 m depth) to investigate compression and collapsible deformation during wetting. The compression in both soils progressed through three stages: slow deformation under low pressure, accelerated deformation under moderate pressure, and decelerated deformation under high pressure. Wetting intensified the compression in the 1 m sample but reduced it in the 25 m sample, with the deformation becoming more sensitive to the initial water content under higher pressures. Collapse tests showed contrasting behaviors: the 1 m sample exhibited collapsibility, while the 25 m sample displayed expansiveness (a negative collapsibility coefficient). Microstructural analysis revealed that the 1 m sample with abundant macropores and overhead structures had a lower structural stability than the 25 sample with more stable, rounded micropores. The wetting-induced deformation was governed by the balance between clay mineral expansion and structural collapse, with collapsibility prevailing when collapse dominated and expansiveness prevailing when expansion was predominant. These findings provide valuable insights into soil–water interactions and support improved land use and management strategies in the loess region.
A Gram-stain-positive, yellow-pigmented, non-motile actinobacterial strain, designated as BIT-GX5 T , was isolated from a sesame husks compost collected in Beijing, PR China. This bacterium was found to be able to grow in the temperature range from 16 to 50 °C and had an optimal growth temperature at 45 °C. Its taxonomic position was analysed using a polyphasic approach. The 16S rRNA gene sequence (1482 bp) of strain BIT-GX5 T was most similar to Cellulosimicrobium funkei ATCC BAA-886 T (99.45%), Cellulosimicrobium cellulans LMG 16121 T (99.17%) and Cellulosimicrobium marinum RS-7-4 T (98.75%). The results of phylogenetic analyses, based on the 16S rRNA gene, concatenated sequences of five housekeeping genes ( gyrB , rpoB , recA , atpD and trpB ) and genome sequences, placed strain BIT-GX5 T in a separate lineage among the genus Cellulosimicrobium within the family Promicromonosporaceae . The major polar lipids of strain BIT-GX5 T were diphosphatidylglycerol, phosphatidylethanolamine, phosphatidylglycerol, aminophospholipid and aminolipid. The major isoprenoid quinone was MK-9(H 4 ), while the cell-wall sugars were galactose, rhamnose, glucose and mannose. The peptidoglycan type was A4α l -Lys– d -Ser –d -Asp. The major fatty acids were anteiso-C 15:0 and iso-C 15: 0 , which were similar to other members in the genus Cellulosimicrobium. Results of in silico DNA–DNA hybridization and average nucleotide identity calculations plus physiological and biochemical tests exhibited the genotypic and phenotypic differentiation of strain BIT-GX5 T from the other members of the genus Cellulosimicrobium . Therefore, strain BIT-GX5 T is considered to represent a novel species within the genus Cellulosimicrobium , for which the name Cellulosimicrobium composti sp. nov. is proposed. The type strain is BIT-GX5 T (= CGMCC 1.17687 T = KCTC 49391 T ).
When samples have internal structure, we often see a mismatch between the objective optimized during training and the model's goal during inference. For example, in sequence-to-sequence modeling we are interested in high-quality translated sentences, but training typically uses maximum likelihood at the word level. Learning to recognize individual faces from group photos, each captioned with the correct but unordered list of people in it, is another example where a mismatch between training and inference objectives occurs. In both cases, the natural training-time loss would involve a combinatorial problem -- dynamic programming-based global sequence alignment and weighted bipartite graph matching, respectively -- but solutions to combinatorial problems are not differentiable with respect to their input parameters, so surrogate, differentiable losses are used instead. Here, we show how to perform gradient descent over combinatorial optimization algorithms that involve continuous parameters, for example edge weights, and can be efficiently expressed as integer, linear, or mixed-integer linear programs. We demonstrate usefulness of gradient descent over combinatorial optimization in sequence-to-sequence modeling using differentiable encoder-decoder architecture with softmax or Gumbel-softmax, and in weakly supervised learning involving a convolutional, residual feed-forward network for image classification.
Boehmeriasin A is a new phenanthroquinolizidine alkaloid recently isolated from the Boehmeria siamensis Craib (Urticaceae). In vitro biological activity assay demonstrated that this novel compound has wide-range, strong antitumor activity. This study is aimed to determine the effects of boehmeriasin A on breast cancer cell (MDA-MB-231 cell line). Proliferation assay and fluorescence activated cell sorter (FACS) showed that cell growth inhibition and G1 phase arrest of cell cycle were caused by boehmeriasin A. The concentrations resulting in total and 50% growth inhibition are 0.007 and 0.0035 microg/mL, respectively. Exposed in 0.007 microg/mL boehmeriasin A for 12 h, the G1 phase cell percent increased from 44.8% pre-drug treatment to 66.3%. Consistent with G1 arrest and cell growth inhibition, cyclin E2 and cyclin D1 messenger RNA expression in the cell was down-regulated with drug treatment. Then, few apoptotic cells were detected, and most other cells underwent differentiation, which is characterized by specific changes in cell morphology, lots of lipid droplet accumulation, and increasing expression of adipocyte differentiation-related protein. The result first demonstrates that boehmeriasin A potently inhibits the proliferation of breast cancer cell MDA-MB-231 via the G1 phase cell cycle arrest and differentiation induction, and as such, may be considered as candidate chemotherapeutic and/or chemopreventive agent for breast cancer.
Rationale Secondary hypertension is often caused by activation of complex multi‐organ endocrine systems, while renin activity indicated by angiotensins (Angs), aldosterone (ALD) and cortisol (COR) in such systems are generally accepted as its diagnostic markers. As antibody‐based methods cannot offer comparable quantification for these biomarkers, a liquid chromatography (LC)–tandem mass spectrometry (MS/MS)‐based approach was developed to quantify them simultaneously and accurately. Methods Five different beads for magnetic solid‐phase extraction (MSPE) were evaluated towards their enrichment efficiency for these biomarkers. An LC system with optimized elution gradient and a triple‐quadrupole MS with tuned parameters were coupled to quantitatively monitor the extracted analytes. The method performance was further examined such as linearity, precision, stability, recovery rate and matrix effect. Based on the developed method, the abundance of Ang II, ALD and COR in plasma was measured and the quantification was compared with that derived from commercial ELISA kits. Results As compared with other MSPEs, Angs, ALD and COR were highly enriched by the HLB magnetic beads with satisfactory recoveries. These analytes were simultaneously quantified by LC/MS/MS and all the method parameters for quantification were well matched with the requirements of clinical testing. Comparison of the quantitative results derived from ELISA and LC/MS/MS exhibited that the two methods offered basically comparable values with Pearson r values at 0.896, 0.895 and 0.835, respectively. The stability test for plasma Angs at room temperature indicated that the abundance of Ang II was relatively stable within 3 h, whereas that of Ang I and Ang 1–7 was time‐dependently changed. Conclusions Coupling of HLB beads and LC/MS/MS thus enables simultaneous quantification of a set of biomarkers related to secondary hypertension.
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