Locally Compact Research Articles

De novo design of mIDH1 inhibitors by integrating deep learning and molecular modeling.

Mutations in the IDH1 gene have been shown to be an important driver in the development of acute myeloid leukemia, gliomas and certain solid tumors, which is a promising target for cancer therapy. Bidirectional recurrent neural network (BRNN) and scaffold hopping methods were used to generate new compounds, which were evaluated by principal components analysis, quantitative estimate of drug-likeness, synthetic accessibility analysis and molecular docking. ADME prediction, molecular docking and molecular dynamics simulations were used to screen candidate compounds and assess their binding affinity and binding stability with mutant IDH1 (mIDH1). BRNN and scaffold hopping methods generated 3890 and 3680 new compounds, respectively. The molecules generated by the BRNN performed better in terms of molecular diversity, druggability, synthetic accessibility and docking score. From the 3890 compounds generated by the BRNN model, 10 structurally diverse drug candidates with great docking score were preserved. Molecular dynamics simulations showed that the RMSD of the four systems, M1, M2, M3 and M6, remained stable, with local flexibility and compactness similar to the positive drug. The binding free energy results indicated that compound M1 exhibited the best binding properties in all energy aspects and was the best candidate molecule among the 10 compounds. In present study, compounds M1, M2, M3 and M6 generated by BRNN exhibited optimal binding properties. This study is the first attempt to use deep learning to design mIDH1 inhibitors, which provides theoretical guidance for the design of mIDH1 inhibitors.

INNOVATIVE APPROACH TO ENSURING THE QUALITY OF GAS TURBINE ENGINE PARTS PRODUCED BY SELECTIVE LASER SINTERING FOR UAV

The research objects are gas turbine engines parts, manufactured using an innovative method of additive manufacturing – selective laser sintering. The main problem solved in this work is the low quality of the surface layer and the residual porosity of the parts obtained by this method, which significantly limits their operational characteristics and durability. As a result of the experimental studies, rational operating parameters of diamond smoothing were established. This allowed to significantly improve the surface quality and increase the operational characteristics of parts made of heat-resistant alloys INCONEL 718 and an intermetallic alloy based on titanium aluminide OX45-3ODS. The effectiveness of diamond smoothing is explained by local plastic deformation and compaction of the surface layer of parts under the influence of high contact pressures and temperatures. This leads to a significant reduction in surface roughness, an increase in the surface hardness due to strain hardening and a significant reduction in the size and number of residual pores. A characteristic feature of the obtained results is the ability to control the quality parameters of the surface layer by varying the diamond smoothing operating parameters – smoothing force, feed, radius, and geometry of the smoother's working part. The established regularities of the smoothing operating parameters have an impact on the quality characteristics of the surface. This information can be utilized in the development of highly efficient technological processes for the production and restoration of gas turbine engines, critical components of unmanned aerial vehicles, obtained through selective laser sintering. Implementing the elaborated technological recommendations will permit broadening the range of goods produced by additive manufacturing and enhancing their capacity and dependability during operation under conditions of cyclical loads and extreme temperatures.

Non-destructive compaction evaluation and comparison of different asphalt centerline longitudinal joints

Longitudinal joint quality is critical to the service life of asphalt pavements. Maintaining failed joints of asphalt pavements is a challenge for many highway agencies. Long-term performance issues of flexible pavements may result from a poorly constructed joint; the low-density joint can prematurely deteriorate an otherwise sound pavement. The longitudinal joint is built using different geometries, rolling patterns, and construction techniques, all involving risk in achieving a well-compacted joint. Conventional quality control (QC) and quality assurance (QA) testing (using cores or density gauges) provide limited coverage due to their spot-test nature. Using conventional QC/QA methods involves the risk of accepting a poorly constructed longitudinal joint at the time of construction. This study used continuous data from the non-destructive dielectric profiling system (DPS) to identify compaction ability differences between the various joint types and construction techniques. The analysis suggests avoiding constructing an unconfined joint when possible. Percent within limits (PWL) analysis shows that any joint geometry could produce minimal compaction differences between the joint and the mat. However, if an unconfined joint needs to be constructed, a portion of the unconfined joint should be cut back before paving the adjacent lane. Such a cutback technique can result in better unconfined joint compaction. Further, PWL results showed that using a smaller subsection/sublot can isolate local compaction issues; a 100 ft sublot length is preferable for PWL analysis when utilizing DPS for compaction evaluation.

Physical and Mechanical Properties of Local Carbon Materials and Warm Compaction Method on the Production of Current Collectors for Light Rail Transit (LRT) Applications

The purpose of this study is to investigate the physical and mechanical properties of local carbon materials and the warm compaction method in the production of current collectors for light rail transit (LRT) applications. The problem here is that the current collectors used by the railway industry in Malaysia for the LRT are still imported from foreign countries which is very costly. Furthermore, the production method of commercial current collectors, namely C-Cu composites, is compact and sintered, which also results in relatively high costs. Therefore, this study focuses on replacing the old materials and methods of commercial current collector production with new materials and methods. This study used a local carbon, which is the kernel shell of oil palm as the main carbon for the production of current collectors. The compact and sintered production methods are then replaced by warm compaction and post-heating methods. The current collectors that had been produced are then cut into several samples to allow them to be tested in anumber of physical and mechanical tests. Based on the test results, when using these new materials and methods, the density and hardness were observed to be slightly lower at 1.81 g/cm3 and 122.6 HRR compared to the commercial current collectors, which have a density of 2.2 g/cm3 and 126.9 HRR. Meanwhile, in the transverse rupture strength (TRS) and resistivity tests, the warm compaction method based on oil palm kernel shell demonstrated higher values of 175.1 MPa and 1631 Ω-cm, respectively, compared to the commercial current collectors which showed values of 58.71 MPa and 598.77 Ω-cm. In conclusion, there are various advantages and disadvantages between the new current collectors and the commercial current collectors in terms of mechanical as well as physical characteristics. Therefore, various improvements and suggestions need to be made in order to produce physically and mechanically better current collectors to be used in LRT applications.

High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws

This paper proposes high-order accurate, oscillation-eliminating, Hermite weighted essentially non-oscillatory (OE-HWENO) finite volume schemes for hyperbolic conservation laws, motivated by the oscillation-eliminating (OE) discontinuous Galerkin schemes recently proposed in [M. Peng, Z. Sun, and K. Wu, 2024 [30]]. The OE-HWENO schemes incorporate an OE procedure after each Runge–Kutta stage, by dampening the first-order moments of the HWENO solution to suppress spurious oscillations without any problem-dependent parameter. The OE procedure acts as a moment filter and is derived from the solution operator of a novel damping equation, which is exactly solved without any discretization. Thanks to this distinctive feature, the OE-HWENO method remains stable with a normal CFL number, even for strong shocks resulting in highly stiff damping terms. To ensure the essentially non-oscillatory property of the OE-HWENO method across problems with varying scales and wave speeds, we design a scale-invariant and evolution-invariant damping equation and propose a generic dimensionless transformation for HWENO reconstruction. The OE-HWENO method offers several notable advantages over existing HWENO methods. First, the OE procedure is highly efficient and straightforward to implement, requiring only simple multiplication of first-order moments by a damping factor. Furthermore, we rigorously prove that the OE procedure maintains the high-order accuracy and local compactness of the original HWENO schemes and demonstrate that it does not compromise the spectral properties via the approximate dispersion relation for smooth solutions. Notably, the proposed OE procedure is non-intrusive, enabling seamless integration as an independent module into existing HWENO codes. Finally, we rigorously analyze the bound-preserving (BP) property of the OE-HWENO method using the optimal cell average decomposition approach [S. Cui, S. Ding, and K. Wu, 2024 [8]], which relaxes the theoretical BP constraint for time step-size and reduces the number of decomposition points, thereby further enhancing efficiency. Extensive benchmarks validate the accuracy, efficiency, high resolution, and robustness of the OE-HWENO method.

Spatial Chromosome Organization and Adaptation of Escherichia coli under Heat Stress.

The spatial organization of bacterial chromosomes is crucial for cellular functions. It remains unclear how bacterial chromosomes adapt to high-temperature stress. This study delves into the 3D genome architecture and transcriptomic responses of Escherichia coli under heat-stress conditions to unravel the intricate interplay between the chromosome structure and environmental cues. By examining the role of macrodomains, chromosome interaction domains (CIDs), and nucleoid-associated proteins (NAPs), this work unveils the dynamic changes in chromosome conformation and gene expression patterns induced by high-temperature stress. It was observed that, under heat stress, the short-range interaction frequency of the chromosomes decreased, while the long-range interaction frequency of the Ter macrodomain increased. Furthermore, two metrics, namely, Global Compactness (GC) and Local Compactness (LC), were devised to measure and compare the compactness of the chromosomes based on their 3D structure models. The findings in this work shed light on the molecular mechanisms underlying thermal adaptation and chromosomal organization in bacterial cells, offering valuable insights into the complex inter-relationships between environmental stimuli and genomic responses.

Holocene relative sea-level variation and coastal changes in the Bay of Cádiz: New insights on the influence of local subsidence and glacial hydro-isostatic adjustments

The Bay of Cádiz is located in South-western Spain (Andalusia region) and constitutes an example of a typical estuarine salt marsh environment. In this study we reconstruct its Holocene morpho-evolution and relative sea-level change history by assembling a geodatabase of geological sea-level markers derived from boreholes and bibliographic data, standardized to the most recent international guidelines for RSL studies. The identified high-precision sea-level index points were compared to a number of new site-specific glacio-hydro-isostatic adjustment (GIA) models in order to disentangle potential components which influenced the sea-level evolution and finally obtain the vertical displacement (VD) trends that affect this coastal area by using a Bayesian statistical approach including Monte Carlo simulations. In general, the whole area was affected by overall subsidence related to the local sediment compaction, which had an impact on the morpho-evolution of the different zones with a variable entity and completely outclassed the GIA-driven component. Between 6.7 and 3.0 ka BP, the northern sector of the bay was characterized by subsidence rates of about - 0.65 mm/yr while, during the last 3.0 ka, the general trend appears to be homogeneous for both the main sectors of the bay with an average subsidence rate of - 1.6 mm/yr. The Holocene RSL curve from the Gulf of Cádiz aligns with past reconstructions, revealing subtle differential trends in subsidence rates in the northern and southern sectors of the Bay of Cádiz due to varying substratum.

Sections of Fell bundles over étale groupoids

We construct the reduced and essential C*-algebra of a Fell bundle over an étale groupoid (in full generality, without any second countability, local compactness or Hausdorff assumptions, even on the unit space) directly from sections under convolution. This eliminates the j-map commonly seen in the groupoid and Fell bundle C*-algebra literature. We further show how multiplier algebras and other Banach *-bimodules can again be constructed directly from sections. Finally, we extend Varela's morphisms from C*-bundles to Fell bundles, thus making the reduced C*-algebra construction functorial.

Protein ensemble modeling and analysis with MMMx.

Proteins, especially of eukaryotes, often have disordered domains and may contain multiple folded domains whose relative spatial arrangement is distributed. The MMMx ensemble modeling and analysis toolbox (https://github.com/gjeschke/MMMx) can support the design of experiments to characterize the distributed structure of such proteins, starting from AlphaFold2 predictions or folded domain structures. Weak order can be analyzed with reference to a random coil model or to peptide chains that match the residue-specific Ramachandran angle distribution of the loop regions and are otherwise unrestrained. The deviation of the mean square end-to-end distance of chain sections from their average over sections of the same sequence length reveals localized compaction or expansion of the chain. The shape sampled by disordered chains is visualized by superposition in the principal axes frame of their inertia tensor. Ensembles of different sizes and with weighted conformers can be compared based on a similarity parameter that abstracts from the ensemble width.

Histone variant H2A.Z and linker histone H1 influence chromosome condensation in Saccharomyces cerevisiae.

Chromosome condensation is essential for the fidelity of chromosome segregation during mitosis and meiosis. Condensation is associated both with local changes in nucleosome structure and larger-scale alterations in chromosome topology mediated by the condensin complex. We examined the influence of linker histone H1 and variant histone H2A.Z on chromosome condensation in budding yeast cells. Linker histone H1 has been implicated in local and global compaction of chromatin in multiple eukaryotes, but we observe normal condensation of the rDNA locus in yeast strains lacking H1. However, deletion of the yeast HTZ1 gene, coding for variant histone H2A.Z, causes a significant defect in rDNA condensation. Loss of H2A.Z does not change condensin association with the rDNA locus or significantly affect condensin mRNA levels. Prior studies reported that several phenotypes caused by loss of H2A.Z are suppressed by eliminating Swr1, a key component of the SWR complex that deposits H2A.Z in chromatin. We observe that an htz1Δ swr1Δ strain has near-normal rDNA condensation. Unexpectedly, we find that elimination of the linker histone H1 can also suppress the rDNA condensation defect of htz1Δ strains. Our experiments demonstrate that histone H2A.Z promotes chromosome condensation, in part by counteracting activities of histone H1 and the SWR complex.

Exploring the Mpemba effect: a universal ice pressing enables porous ceramics.

Piezoceramics with global porosity and local compaction are highly desired to exploit the combination of mechanical and electrical properties. However, achieving such a functional combination is challenging because of the lack of techniques for applying uniform pressure inside porous ceramic green parts. Nature provides many examples of generating strong forces inside the macro and micro channels via the state transformation of water. Inspired by these phenomena, we present a technique of "ice and fire", that is, water freezing (ice pressing) and high-temperature sintering (fire), to produce ideal porous piezoceramics. We introduce a new compaction method called the "ice pressing method", which manipulates liquid phase transition for compaction. This method has several advantages, including uniform pressure distribution, a wide pressure range, high effectiveness, and selective freezing. It can generate an ultrahigh pressure of up to 180 MPa on the piezoceramic green skeletons in minutes while retaining their functional pore structures. By exploiting the Mpemba phenomenon, we further accelerate the compaction procedure by 11%. The first ice-pressed and second fire-consolidated lead zirconate titanate (PZT) ceramics are highly densified and exhibit an outstanding piezoelectric response (d33 = 531 pC N-1), comparable to conventional pressed bulk counterparts and 10-20 times higher than those of unpressed materials. The novel ice pressing method breaks the limitation of lacking a compaction technique for porous ceramics. The versatile and effective ice pressing method is a green and low-cost route promoting applications in sensors, acoustics, water filtration, catalyst substrates, and energy harvesting.

Nonequilibrium switching of segmental states can influence compaction of chromatin.

Knowledge about the dynamic nature of chromatin organization is essential to understand the regulation of processes like DNA transcription and repair. The existing models of chromatin assume that protein organization and chemical states along chromatin are static and the 3D organization is purely a result of protein-mediated intra-chromatin interactions. Here we present a new hypothesis that certain nonequilibrium processes, such as switching of chemical and physical states due to nucleosome assembly/disassembly or gene repression/activation, can also simultaneously influence chromatin configurations. To understand the implications of this inherent nonequilibrium switching, we present a block copolymer model of chromatin, with switching of its segmental states between two states, mimicking active/repressed or protein unbound/bound states. We show that competition between switching timescale Tt, polymer relaxation timescale τp, and segmental relaxation timescale τs can lead to non-trivial changes in chromatin organization, leading to changes in local compaction and contact probabilities. As a function of the switching timescale, the radius of gyration of chromatin shows a non-monotonic behavior with a prominent minimum when Tt ≈ τp and a maximum when Tt ≈ τs. We find that polymers with a small segment length exhibit a more compact structure than those with larger segment lengths. We also find that the switching can lead to higher contact probability and better mixing of far-away segments. Our study also shows that the nature of the distribution of chromatin clusters varies widely as we change the switching rate.

NUMERICAL THREE-DIMENSIONAL MODEL OF ULTRASONIC COAGULATION OF AEROSOL PARTICLES IN VORTEX ACOUSTIC STREAMING

Separation of highly dispersed systems with huge liquid-gas or liquid-solid interfaces is relevant for practical tasks of gas purification from the most highly dispersed and difficult-to-detect dispersed fraction PM2.5, and separation of nanoparticles (including their small agglomerates) in fine chemical technology processes. One of the most effective ways to separate highly dispersed systems with a large interface surface is to combine each of the closed subsurfaces (surfaces of individual dispersed particles) under the influence of hydrodynamic effects in the gas phase, arising both near the interface surfaces and at a considerable distance from them, due to the superposition of ultrasonic vibrations. Since the efficiency of ultrasonic coagulation decreases with a large distance between closed subsurfaces from each other in PM2.5 aerosol and the small size of these surfaces, it is necessary to create conditions for the emergence of new nonlinear effects that contribute to the local compaction of the dispersed fraction. In a resonant and significantly inhomogeneous ultrasonic field (with a scale of inhomogeneity on the order of the wavelength), vortex acoustic flows arise, which, due to inertial forces, locally compact the dispersed phase in the form of an increase in the concentration of aerosol particles. A numerical model of ultrasonic coagulation of PM2.5 aerosol particles in three-dimensional (3D) vortex acoustic streaming is proposed in this paper. The model is designed to identify the possibility of increasing the efficiency of ultrasonic coagulation in 3D streaming by virtue of the following mechanisms: (1) local increase in concentration caused by the inertial transfer of particles to the periphery of 3D vortices in the gas phase; (2) increase in the frequency of particle collisions due to 3D turbulent disturbances in ultrasonic fields; and (3) increase in productivity and ensuring uninterrupted implementation of the process in a flow mode owing to transfer of particles between the streamlines of the main vortices initiated by ultrasonic vibrations. The listed mechanisms for increasing the efficiency of coagulation in 3D streaming are taken into consideration by introducing two stream functions, considering turbulent chaotic disturbances of the flow resulting in dispersion of particle velocities. It was possible to establish based on numerical analysis of the model using the example of PM2.5 that laminar vortex flows begin to influence at sound pressure level from 160-165 dB, and turbulent disturbances make an additional contribution in the range of sound pressure levels from 140-170 dB. At the same time, as a result of 3D turbulent disturbances, the efficiency of coagulation reaches almost 100% at a sound pressure level 5 dB lower than with laminar flows (sound pressure amplitude, 3 times lower).

Hydraulic properties of sediments from the GC955 gas hydrate reservoir in the Gulf of Mexico

The economic feasibility of gas production from hydrate deposits is critical for hydrate to become an energy resource. Permeability in hydrate-bearing sediments dictates gas and water flow rates and needs to be accurately evaluated. Published permeability studies of hydrate-bearing sediments mostly quantify vertical permeability; however, the flow is mainly horizontal during gas production in layered reservoirs. Additionally, ASTM standards require a hydraulic gradient of 10–30 to be used during laboratory permeability measurements, but the gradient is much higher in the field, particularly near a production well. To address these issues, this study focuses on the hydraulic properties of a sandy silt subsample of the hydrate reservoir and a clayey silt subsample of the fine-grained, hydrate-free interbed recovered from a GC955 deep-water Gulf of Mexico gas hydrate reservoir. We characterize the sediment pore space with water retention curves for both hydrate-free and hydrate-bearing samples (hydrate saturation, Sh =80 %). Vertical deformation with increasing stress is also quantified while consolidating the samples to the 4 MPa in situ vertical effective stress. The customized permeameter measures both the horizontal and vertical permeability with increasing stress. Results show that high hydraulic gradients lower permeability in the flow direction, possibly due to increased flow tortuosity and local sediment compaction from the high seepage force. Assuming a single permeability value, even though hydraulic gradients decrease with distance from the well, is not realistic for field estimations. The results highlight that permeability anisotropy, hydrate saturation, stress conditions, and hydraulic gradient all substantially impact reservoir permeability during production.

Development of a Sustainable Maintenance Strategy for Forest Road Wearing Courses in Different Climate Zones

This study was done to determine the appropriate maintenance strategies for the deteriorating gravel forest roads in the Mediterranean, sub-humid and semi-arid climates. Unmanned Aerial Vehicle (UAV) was used to monitor Unpaved Road Condition Index (UPCI), immediately after maintenance activities and seasonally in one year. The deterioration time of the wearing course was predicted using Markov chain analysis. Results showed that roads in sub-humid climates presented lower UPCI (7.19) compared to the Mediterranean (7.81) and semi-arid (8.82) climates. When roads were maintained by a high-budget strategy, deterioration time was longer than when other strategies were used. The cost-effectiveness (CE) value of the low-budget strategy was more favorable than different strategies in all traffic levels of the Mediterranean climate and high-traffic roads in a semi-arid environment. Low-budget maintenance activities include one culvert improvement per 6 km, light blading, and 30 mm layer graveling. In a semi-arid climate, a medium-budget maintenance strategy was more efficient in medium and low-traffic roads. Medium, high, and low-budget maintenance strategies were efficient in high, medium, and low-traffic roads in sub-humid climates. High-budget maintenance activities include one culvert improvement per 4 km, heavy blading and local compaction, and 60 mm layer graveling. Overall, it was concluded that monitoring UPCI over time and probability analysis using time series is helpful for a sustainable and long-term management of forest roads.

Continuity-sets of pullback random attractors for discrete porous media equations with colored noise

For a random non-autonomous porous media lattice system driven by nonlinear colored noise, we prove the unique existence and local compactness of a pullback random attractor. We then mainly study the continuity-set (the set of all points of continuity) of the pullback random attractor on the time-sample plane with respect to the Hausdorff metric. With some calculations, we find that the continuity-set has four geometrical numerical features:(1) The continuity-set is residual and dense in the time-sample plane.(2) The continuity-set is composed of infinitely many diagonal rays (with slope one).(3) The continuity-set is dense in any non-diagonal line (with an inclined angle not being 45∘).(4) Restrictions of the continuity-set on diamonds are composed of parallel line segments with increasing numbers.

Crucial feature capture and discrimination for limited training data SAR ATR

Deep learning-based methods have demonstrated exceptional performance in the field of synthetic aperture radar automatic target recognition (SAR ATR). However, obtaining a sufficient number of labeled SAR images remains a significant challenge that can negatively affect the performance of these methods. This is because most deep learning models use the entire target image as input. However, but research has shown that with limited training data, the model may not be able to capture discriminative regions of the image. Instead, they might focus on more useless even harmful image regions for recognition, leading to poor recognition results. In this study, we propose a novel SAR ATR framework that addresses the limitation of limited training data. The proposed framework primarily comprises a global assisted branch, locally enhanced branch, feature capture module, and feature discrimination module. The global-assisted branch conducts an initial recognition and provides a loss based on the entire SAR image during each training epoch and the feature capture module automatically segments and captures crucial image regions for current recognition, which we refer to as the “golden key” of the image. The local enhanced branch then performs another recognition and provides another loss function based on the image parts. Instead of updating the model with two basic recognition losses to roughly search for and capture crucial image parts, a feature discrimination module is proposed to combine the global and local branches in a subtle manner to improve local feature separability or compactness for similar inter-class or dissimilar inner-class sample pairs in global features. This adaptively forced the model to capture more crucial image parts and extract more effective features. Experimental results and comparisons of the MSTAR and OpenSARship datasets indicated that the proposed method achieves superior recognition performance compared to existing methods. The effectiveness of our method was further demonstrated through the visualization of the golden key of the testing images and the recognition performance in ablation experiments. We will release our codes and more experimental results at https://github.com/cwwangSARATR/SARATR_FeaCapture_Discrimination.

Evolution of cavity formation in nontuberculosis mycobacteriosis of the lungs

The results of a long – term observation from practice are presented, which showed the gradual formation of the destruction cavity in a patient with limited focal and peribronchial fibrosis of the lung tissue. Patient H., 54 years old for more than twenty years, was observed by a pulmonologist at the place of residence with a diagnosis of chronic bronchitis with frequent annual exacerbations. She was admitted to the clinic of the FSBSI "CRIT" with complaints of pronounced weakness, fatigue, shortness of breath, prolonged subfebrile temperature mainly at night, cough with difficult-to-separate mucus of a mucous nature. A retrospective analysis of computed tomography of the chest revealed a consistent transformation of local focal peribronchial compaction in the middle lobe of the right lung into a limited area of bronchiectasia and the formation of a small cystic cavity with widespread zones of bilateral pneumonic infiltration. This observation shows the practical significance of CT research in understanding the mechanisms of formation of bronchiectatic cystic cavity in non-tuberculosis mycobacteriosis of the lungs.

Equivalence of minimax and viscosity solutions of path-dependent Hamilton–Jacobi equations

In the paper, we consider a path-dependent Hamilton–Jacobi equation with coinvariant derivatives over the space of continuous functions. Such equations arise from optimal control problems and differential games for time-delay systems. We study generalized solutions of the considered Hamilton–Jacobi equation both in the minimax and in the viscosity sense. A minimax solution is defined as a functional which epigraph and subgraph satisfy certain conditions of weak invariance, while a viscosity solution is defined in terms of a pair of inequalities for coinvariant sub- and supergradients. We prove that these two notions are equivalent, which is the main result of the paper. As a corollary, we obtain comparison and uniqueness results for viscosity solutions of a Cauchy problem for the considered Hamilton–Jacobi equation and a right-end boundary condition. The proof of the main result is based on a certain property of the coinvariant subdifferential. To establish this property, we develop a technique going back to the proofs of multidirectional mean-value inequalities. In particular, the absence of the local compactness property of the underlying continuous function space is overcome by using Borwein–Preiss variational principle with an appropriate gauge-type functional.

Evaluating the role of the nuclear microenvironment in gene function by population-based modeling.

The nuclear folding of chromosomes relative to nuclear bodies is an integral part of gene function. Here, we demonstrate that population-based modeling-from ensemble Hi-C data-provides a detailed description of the nuclear microenvironment of genes and its role in gene function. We define the microenvironment by the subnuclear positions of genomic regions with respect to nuclear bodies, local chromatin compaction, and preferences in chromatin compartmentalization. These structural descriptors are determined in single-cell models, thereby revealing the structural variability between cells. We demonstrate that the microenvironment of a genomic region is linked to its functional potential in gene transcription, replication, and chromatin compartmentalization. Some chromatin regions feature a strong preference for a single microenvironment, due to association with specific nuclear bodies in most cells. Other chromatin shows high structural variability, which is a strong indicator of functional heterogeneity. Moreover, we identify specialized nuclear microenvironments, which distinguish chromatin in different functional states and reveal a key role of nuclear speckles in chromosome organization. We demonstrate that our method produces highly predictive three-dimensional genome structures, which accurately reproduce data from a variety of orthogonal experiments, thus considerably expanding the range of Hi-C data analysis.