Discrete Domain Research Articles

Homotopy perturbation method and its convergence analysis for nonlinear collisional fragmentation equations

The exploration of collisional fragmentation pheno-mena remains largely unexplored, yet it holds considerable importance in numerous engineering and physical processes. Given the nonlinear nature of the governing equation, only a limited number of analytical solutions for the number density function corresponding to empirical kernels are available in the literature. This article introduces a semi-analytical approach using the homotopy perturbation method to obtain series solutions for the nonlinear collisional fragmentation equation. The method presented here can be readily adapted to solve both linear and nonlinear integral equations, eliminating the need for domain discretization. To gain deeper insights intothe accuracy of the proposed method, a convergence analysis is conducted. This analysis employs the concept of contractive mapping within the Banach space, a well-established technique universally acknowledged for ensuring convergence. Various collisional kernels (product and polymerization kernels), breakage distribution functions (binary and multiple breakage) and various initial particle distributions are considered to obtain the new series solutions. The obtained results are successfully compared against finite volume method [26] solutions in terms of number density functions and their moments. The error between the exact and obtained series solutions is shown in plots and tables to confirm the applicability and accuracy of the proposed method.

Organizing Dots and Lines: Eastern Hui and the Adaptation of the CCP's Nationalities Work in the Revolutionary Era

AbstractAlthough ethnic governance in the People's Republic of China is often portrayed as a matter of controlling “minority nationalities” in the country's frontier regions, the ethnic affairs bureaucracy operates in every province. The origins of “nationalities work” as a discrete domain of governance can be traced to the Chinese Communist Party's efforts to mobilize scattered Hui communities in the eastern provinces of Shandong and Hebei in the 1930s–1940s. Thanks to the initiative of Hui Communists, local Party leaders came to understand that Hui were not simply scattered but interconnected. They adapted and replicated organizational methods to exploit Hui networks for gathering intelligence, smuggling goods and penetrating enemy-controlled cities. This history offers an instructive case of adaptive governance in the revolutionary period and the role of ethnic minority cadres in policy entrepreneurship. It also underscores the importance of the Party's experience in eastern China in the study of Chinese ethnic policy.

The s-version finite element method for non-linear material problems

This study intended to extend the s-version of the finite element method (s-version FEM) to cope with elastic–plastic problems. Compared with the conventional FEM, the s-version FEM, which overlays a set of local mesh with fine element size representing irregular features over the conventional FE mesh with coarse element size, can considerably simplify issues in domain discretisation with fewer degrees of freedom and provide accurate numerical predictions. However, most applications of the s-version FEM were limited to elastic problems only, leaving its applications to elastic–plastic problems almost blank owing to insufficient instructions on stress update when plasticity sets in. To address these issues, detailed instructions and formulations to cope with plasticity problems with the s-version FEM were presented for its first time. The recursive element subdivision technique was implemented to generalise its application where local elements intersect with global element edges. A 3D stress concentration problem with linear/non-linear material properties was analysed; their numerical results were compared with the exact solutions and those obtained from the conventional FEM with very fine elements. The comparison highlights the flexibility of the s-version FEM in domain discretisation and its superior accuracy in numerical calculations, thereby exhibiting high potential applications in structural integrity assessment with complex structures, geometric defects, and material non-linearity.

A comparative study to solve fractional initial value problems in discrete domain

Abstract In this article, we used some methods to solve Riemann-type fractional difference equations. Firstly, we use a method that is a composite method based on the successive approximation method with the Sumudu transform. Secondly, we use a method that is a composite method that consists of the homotopic perturbation method with the Sumudu transform. It was found that the results obtained from these combined methods are identical when compared. We also provided theories and illustrative examples to support the research findings.

Evaluating the parameter sensitivity and impact of hydrologic modeling decisions on flood simulations

Recent studies argue that hydrological models must be configured for the specific objectives they need to address. Model configuration involves multiple model decision steps, such as choice of model structure, spatial discretization, spatial representation of forcing and performance metrics to calibrate them. We investigated the influence of each of the decisions in turn in a standardized framework to understand how differences in these decisions impact flood simulations. For this purpose, we used the capability of Structure for Unifying Multiple Modeling Alternatives (SUMMA) model as it allows a straightforward comparison of different model structure choices and can easily be reconfigured for different spatial organization. We also employed a sequential sensitivity analysis using the Efficient Elementary Effect (EEE) method to select the sensitive parameters for each model structure considered in this study. This allowed us to check if the dominant hydrological process of the catchment can be captured irrespective of the model structure choice. Identification of the most sensitive parameters also helped us to scale down the dimensionality of the problem both in terms of computational demand and complexity. Based on the various choices of model decisions, 36 unique model configurations are constructed and each of them are separately calibrated by the performance metrics. The impact and relative importance of modeling decisions are quantified by Analysis of Variance(ANOVA) and effect size respectively. As a test case, we use accurate simulation of flood peaks (expressed as deviation in peak flow, deviation in peak time and relative volume error) that occurred in the Netravathi basin of Karnataka, India to study the impact of the model decisions. The extensive sensitivity analysis and model calibration required for the study is carried out by parallel processing using a supercomputer. For floods, the choice of spatial discretization of the modeling domain is the most impacting decision, followed by the choice of objective function during calibration, model structure and spatial representation of forcing, respectively, for the catchment. The results provide key insights regarding the ideal option a modeler must choose for each modeling decision for simulating floods in Netravathi. More generally, this study shows that model configuration decisions that are anecdotally often made based on convenience or habit can strongly impact simulation accuracy for specific modeling purposes. Alongside the need to quantify more traditional uncertainty sources, such as data and parameter uncertainty, there is a need to quantify the impact of these model configuration decisions.

A Review of Semantic Application of MI Theory and Effects for Teacher Training

The notion of “multiple intelligences” (MI) was established by Howard Gardner, a psychologist from the United States, during the latter part of the 1970s and the early part of the 1980s. Gardner introduced the concept of MI in his 1983 publication titled Frames of Mind: The Theory of Multiple Intelligences, positing that individuals possess unique cognitive abilities across eight discrete domains. As per the theory, there exist nine discrete categories of intelligence, such as logical-mathematical, visual-spatial, musical-rhythmic, verbal-linguistic, bodily-kinesthetic, intrapersonal, interpersonal, existential, and naturalistic. Individuals construct their distinct cognitive frameworks by engaging in activities that are highly valued within their respective cultural contexts. The present article furnishes a comprehensive outline of the rationales and plausible scenarios for deliberating MI theory with pre-service educators during their teacher training. This study examines the significance of Universal Design for Learning (UDL) and comparable models in the context of teacher training, taking into account the distinctions between the semantic theoretical foundations of intelligence in Multiple Intelligences (MI) theory and learning styles theory.

The boundary of a graph and its isoperimetric inequality

We define, for any graph G=(V,E), a boundary ∂G⊆V. The definition coincides with what one would expected for the discretization of (sufficiently nice) Euclidean domains and contains all vertices from the Chartrand, Erwin, Johns & Zhang boundary. Moreover, it satisfies an isoperimetric principle stating that graphs with many vertices have a large boundary unless they contain long paths: we show that for graphs with maximaldegree Δ |∂G|≥12Δ|V|diam(G).For graphs discretizing Euclidean domains, one has diam(G)∼|V|1/d and recovers the scaling of the classical Euclidean isoperimetric principle.

Active maintenance of CD8+ T cell naivety through regulation of global genome architecture

The differentiation of naive CD8+ T lymphocytes into cytotoxic effector and memory CTL results in large-scale changes in transcriptional and phenotypic profiles. Little is known about how large-scale changes in genome organization underpin these transcriptional programs. We use Hi-C to map changes in the spatial organization of long-range genome contacts within naive, effector, and memory virus-specific CD8+ Tcells. We observe that the architecture of the naive CD8+ Tcell genome is distinct from effector and memory genome configurations, with extensive changes within discrete functional chromatin domains associated with effector/memory differentiation. Deletion of BACH2, or to a lesser extent, reducing SATB1 DNA binding, within naive CD8+ Tcells results in a chromatin architecture more reminiscent of effector/memory states. This suggests that key transcription factors within naive CD8+ Tcells act to restrain Tcell differentiation by actively enforcing a unique naive chromatin state.

Determination of the bone tissue mechanical properties by a numerical-digital method using CT data

Modeling of elements of inhomogeneous media is an actual direction in the study of composite materials and biomechanics objects. The need for research is determined by the insufficient development of methods for describing mechanical parameters, taking into account the anisotropy of materials. In this case, one of the directions is the use of digital prototyping and numerical modeling methods. In the field of biomechanics, the applicability of approaches to numerical modeling based on image data correlates with cases of clinical practice, which is due to the peculiarities of non-destructive testing methods and allows obtaining results that affect the quality of treatment. The paper considers a method for restoring effective mechanical properties of a material based on computational and field experiments. The simulation was based on the finite element method and assumed the use of data from a digital prototype obtained by computed tomography. The restoration of the calculated area was performed by filtering the initial grid relative to the proportion of the content of the material. The presented method makes it possible to restore the effective values of the elastic modulus and tangential modules based on the relationship established within the framework of the approach between the mechanical properties of the material and the loading parameters of the model sample. In the course of the work, the bone organs of pigs were modeled. Animal husbandry and experimental procedures were carried out in compliance with bioethical norms. Physical tests and numerical modeling were carried out under the conditions of bending action. Validation of the obtained distribution of values of the stress-strain state was performed according to the data of full-scale experiments. The presented solution showed a weak dependence of the results (less than 1 %) relative to the degree of discretization of the computational domain, which made it possible to perform calculations using fewer finite elements, avoiding the use of resource-intensive methods to restore the geometry of the sample. The results obtained in the framework of the work correspond to the literature data and determine the true values, the use of which in calculations makes it possible to assess the strength of the elements of an inhomogeneous structure under the action of external loads, taking into account the spatial distribution of the material.

Data-driven solution for supersonic aerodynamics analysis of Perovskite solar cells considering the velocity of sound and Mach number

Due to the use of Perovskite solar cells (PSC) in aerospace applications, so, in this work for the first time, aerodynamic flutter and vibrational analysis of PSC are presented. For modeling the PSCs aerodynamic motion in the mathematical domain, the variational differential quadrature (VDQ) technique is used as a numerical operator for the discretization of various domains. Also, due to improving the stability of the PSC, carbon nanotubes with various distribution patterns as the reinforcement of the metal layer are presented. In this work for modeling the aerodynamics behavior, we use Krumhaar’s modified supersonic piston theory incorporating curvature influence, to simulate the aerodynamic stiffness and damping matrices. Also, for modeling the size effect, a modified couple stress theory with only one length scale factor is suggested. Data-driven solution with the aid of deep neural network with independent variables, input, hidden, and output layers, activation function, neural network’s intrinsic parameters, loss function, and hidden neurons is presented to solve the current applicable structure. The results show that the stability of the system is substantially impacted by the value of the yaw angle, and the link between Mach number and stability is heavily reliant on the value of the yaw angle. Another important outcome is that designing a spherical PSC and increasing its stability should have special attention to the a/b parameter. Also, future engineering research should have special attention that spherical solar cell has the highest natural frequency than other types of solar cells. Other important outcomes of the innovative PSC are presented in the results section for future handbooks on solar cells as sustainable energy.

CREB1 spatio-temporal dynamics within the rat pineal gland

In the rat pineal gland (PG), cyclic AMP responsive element-binding protein 1 (CREB1) participates in the nocturnal melatonin synthesis that rhythmically modulates physiology and behavior. Phosphorylation of CREB1 is one of the key regulatory steps that drives pineal transcription. The spatio-temporal dynamics of CREB1 itself in the different PG cell types have not yet been documented. In this study we analyzed total CREB1 in the rat PG via Western blot and fluorescence immunohistochemistry followed by confocal laser-scanning microscopy and quantitative analysis. Total CREB1 levels remained constant in the PG throughout the light:dark cycle. The distribution pattern of nuclear CREB1 did vary among PG cell types. Pinealocytes emerged to have discrete CREB1 domains within their nucleoplasm that were especially distinct. The number, size, and location of CREB1 foci fluctuated among pinealocytes, within the same PG and among Zeitgeber times (ZTs). A significantly larger dispersion of CREB1-immunoreactive nuclear sites was found at night than during the day. However, the overall transcription activity was mostly conserved between the light and dark phases, as shown by the expression of a particular phosphorylated form of the RNA polymerase II (RNAPII-pSer5CTD). Suppression of the nocturnal norepinephrine pulse by chronic bilateral superior cervical ganglionectomy increased CREB1 dispersion in pinealocyte nuclei at early night, as compared to sham-derived cells. In addition, differences in CREB1 distribution were found between sham-operated and non-operated rats at ZT14. Together, these data suggest that in mature pinealocytes, nuclear CREB1 is subjected to a dynamic spatio-temporal distribution. Further studies are necessary to elucidate the underlying mechanisms and to understand the impact of CREB1 reorganization in the pineal transcriptome.

Method for Adaptive Wavelet Filtering of Speech Signals Based on Daubechies Filters with Minimization of Errors in Finding Optimal Thresholds

The paper deals with the problem of adaptive wavelet filtering of speech signals based on Daubechies filters with minimization of errors in finding optimal threshold values. This approach is similar to estimating a speech signal by averaging it using a kernel that is locally adapted to the smoothness of the signal. In this case, a set of coupled mirror filters decomposes the speech signal in a discrete domain according to the orthogonal Daubechies wavelet basis into several frequency bands. Noise removal of speech signals is performed as a complete cutoff of the wavelet transform coefficients based on the assumption that their small amplitude values are noise. Thus, in the Daubechies wavelet basis, where coefficients with large amplitude correspond to abrupt changes in the speech signal, such processing preserves only the intermittent components originating from the input speech signal without adding other components caused by noise. In general, by equating small coefficients to zero, we perform adaptive smoothing that depends on the smoothness of the input speech signal. By keeping the coefficients of large amplitude, we avoid smoothing out sharp drops and preserve local features. Performing this procedure on several scales leads to a gradual reduction of the noise effect on both piecewise smooth and discontinuous parts of the speech signal. In view of this, the main task of the study is to adaptively generate micro-local thresholds, which will reduce the impact of additive noise on the pure form of the speech signal, and preserve significant wavelet coefficients of large amplitude that characterize the local features of the speech signal. Thus, as a result of our work, we have proved the feasibility of developing the presented method of wavelet filtering of speech signals with adaptive thresholds based on Daubechies wavelet analysis, which minimizes the loss of speech intelligibility and allows for noise removal depending on the properties and physical nature of the processed data.

Deep reinforcement learning for the rapid on-demand design of mechanical metamaterials with targeted nonlinear deformation responses

Mechanical metamaterials are artificial materials with unique global properties due to the structural geometry and material composition of their unit cell. Typically, mechanical metamaterial unit cells are designed such that, when tessellated, they exhibit unique mechanical properties such as zero or negative Poisson's ratio and negative stiffness. Beyond these applications, mechanical metamaterials can be used to achieve tailorable nonlinear deformation responses. Computational methods such as gradient-based topology optimization (TO) and size/shape optimization (SSO) can be implemented to design these metamaterials. However, both methods can lead to suboptimal solutions or a lack of generalizability. Therefore, this research used deep reinforcement learning (DRL), a subset of deep machine learning that teaches an agent to complete tasks through interactive experiences, to design mechanical metamaterials with specific nonlinear deformation responses in compression or tension. The agent learned to design the unit cells by sequentially adding material to a discrete design domain and being rewarded for achieving the desired deformation response. After training, the agent successfully designed unit cells to exhibit desired deformation responses not experienced during training. This work shows the potential of DRL as a high-level design tool for a wide array of engineering applications.

Critical power is a key threshold determining the magnitude of post-exercise hypotension in non-hypertensive young males.

The effect of different exercise intensities on the magnitude of post-exercise hypotension has not been rigorously clarified with respect to the metabolic thresholds that partition discrete exercise intensity domains (i.e., critical power and the gas exchange threshold (GET)). We hypothesized that the magnitude of post-exercise hypotension would be greater following isocaloric exercise performed above versus below critical power. Twelve non-hypertensive men completed a ramp incremental exercise test to determine maximal oxygen uptake and the GET, followed by five exhaustive constant load trials to determine critical power and W' (work available above critical power). Subsequently, criterion trials were performed at four discrete intensities matched for total work performed (i.e., isocaloric) to determine the impact of exercise intensity on post-exercise hypotension: 10% above critical power (10%>CP), 10% below critical power (10%<CP), 10% above GET (10%>GET) and 10% below GET (10%<GET). The post-exercise decrease (i.e., the minimum post-exercise values) in mean arterial (10%>CP: -12.7±8.3 vs. 10%<CP: v3.5±2.9mmHg), diastolic (10%>CP: -9.6±9.8 vs. 10%<CP: -1.4±5.0mmHg) and systolic (10%>CP: -23.8±7.0 vs. 10%<CP: -9.9±4.3mmHg) blood pressures were greater following exercise performed 10%>CP compared to all other trials (all P<0.01). No effects of exercise intensity on the magnitude of post-exercise hypotension were observed during exercise performed below critical power (all P>0.05). Critical power represents a threshold above which the magnitude of post-exercise hypotension is greatly augmented. NEW FINDINGS: What is the central questions of this study? What is the influence of exercise intensity on the magnitude of post-exercise hypotension with respect to metabolic thresholds? What is the main finding and its importance? The magnitude of post-exercise hypotension is greatly increased following exercise performed above critical power. However, below critical power, there was no clear effect of exercise intensity on the magnitude of post-exercise hypotension.

Quantum algorithm for smoothed particle hydrodynamics

We present a quantum computing algorithm for the smoothed particle hydrodynamics (SPH) method. We use a normalization procedure to encode the SPH operators and domain discretization in a quantum register. We then perform the SPH summation via an inner product of quantum registers. Using a one-dimensional function, we test the approach in a classical sense for the kernel sum and first and second derivatives of a one-dimensional function, using both the Gaussian and Wendland kernel functions, and compare various register sizes against analytical results. Error convergence is exponentially fast in the number of qubits. We extend the method to solve the one-dimensional advection and diffusion partial differential equations, which are commonly encountered in fluids simulations. This work provides a foundation for a more general SPH algorithm, eventually leading to highly efficient simulations of complex engineering problems on gate-based quantum computers.

Integer-valued polynomials on valuation rings of global fields with prescribed lengths of factorizations

Let V be a valuation ring of a global field K. We show that for all positive integers k and 1 < n_1 le cdots le n_k there exists an integer-valued polynomial on V, that is, an element of {{,textrm{Int},}}(V) = { f in K[X] mid f(V) subseteq V }, which has precisely k essentially different factorizations into irreducible elements of {{,textrm{Int},}}(V) whose lengths are exactly n_1,ldots ,n_k. In fact, we show more, namely that the same result holds true for every discrete valuation domain V with finite residue field such that the quotient field of V admits a valuation ring independent of V whose maximal ideal is principal or whose residue field is finite. If the quotient field of V is a purely transcendental extension of an arbitrary field, this property is satisfied. This solves an open problem proposed by Cahen, Fontana, Frisch and Glaz in these cases.

Continuum Modeling of Gas and Ions Transport in a High-Surface-Area Carbon (HSC) Nanopore

PEM fuel cell (PEMFC) is one of the promising energy conversion devices for emission-free transportation applications. It is beneficial in faster charging and better scalability compared to battery-powered vehicles, making PEMFC a viable option for heavy-duty vehicles which require higher efficiency and longer lifetimes. To economically compete with the combustion engine and improve commercialization, the PEMFC cathode desires optimization in enhancing the utilization of the expensive Pt catalyst. Integration of high-surface-area carbon (HSC) has shown to increase accessible Pt surface by diminishing ionomer poisoning as Pt particles can be loaded inside the nanoscale micropores (<5 nm) that ionomer cannot penetrate due to size restriction. However, separating Pt catalysts from ionomers requires a water pathway to deliver the proton to the interior catalyst surface, leading to RH-dependent electrochemical surface area (ECSA). In this work, we develop a steady-state, isothermal continuum model to study the gas and ions transport within HSC nanopores. The pore is represented as a straight cylindrical channel filled with water with an ionomer domain at the pore mouth serving as a proton reservoir. The ionomer phase contains H+, OH-, and background stationary SO3 - while the water phase only includes H+ and OH-. The Poisson-Nernst-Plank equations describe the flux of ions, and O2 transport is described by Fick’s law. Non-ideal behaviors including nanoconfinement effects and dielectric saturation are considered in the pore water phase, reflected by corrections in ion chemical potentials, diffusion coefficients of transport species, and dielectric constant. The electrical double layer (EDL) at the water-electrode interface is depicted as discrete finite domains applying the Gouy-Chapman-Stern (GCS) theory, with the oxygen reduction reaction (ORR) occurring at a finite reaction plane at the outer Helmholtz plane (OHP) through both acidic and alkaline reaction pathways. Donnan potential drop is solved at the ionomer-pore water interface and governs potential distribution in the pore water phase, further determining ionic concentrations at the catalyst surface and thus the kinetic region of polarization curves. The strong-adsorbed water adlayers due to nanoconfinement effects create a transport barrier for O2 approaching the catalyst surface, leading to higher mass transport resistance. A comparison between a flooded pore scenario (only a water phase exists in the pore) and a wetted pore scenario (the pore wall is covered by a water film while a gas phase also exists in the pore) shows that mass transport is hindered in the flooding pore as O2 dissolves in the pore water through a limited pore-ionomer interfacial area, while pore gas phase in the wetted pore serves as an extra O2 resource. This suggests that the management of HSC water uptake needs to avoid pore flooding while ensuring enough wettability to allow proton transport. The model is expected to couple with HSC pore size distribution measured from experiments and upscale to a cell-level model in future work.

Colorful path detection in vertex-colored temporal

AbstractFinding paths is a fundamental problem in graph theory and algorithm design due to its many applications. Recently, this problem has been considered on temporal graphs, where edges may change over a discrete time domain. The analysis of graphs has also taken into account the relevance of vertex properties, modeled by assigning to vertices labels or colors. In this work, we deal with a problem that, given a static or temporal graph, whose vertices are colored graph looks for a path such that (1) the vertices of the path have distinct colors and (2) that path includes the maximum number of colors. We analyze the approximation complexity of the problem on static and temporal graphs, and we prove an inapproximability bound. Then, we consider the problem on temporal graphs, and we design a heuristic for it. We present an experimental evaluation of our heuristic, both on synthetic and real-world graphs. The experimental results show that for many instances of the problem, our method is able to return near-optimal solutions.

An ensemble learning approach for resampling forgery detection using Markov process

Resampling is an extremely well-known technique performed for Image forgery detection. It includes the changes in the content of a picture in terms of rotation, stretching/zooming, and shrinking, to frame a forged picture that is a localized forgery in comparison to the original picture. With the wrong intention, resampling forgery has been increased day by day, and its negative impact has been increased in criminology, law enforcement, forensics, research etc. Accordingly, the interest in the algorithm of image resampling forgery detection is significantly developed in image forensics. In this paper, a novel image resampling forgery detection technique has been proposed. In the proposed technique, two types of Markov feature with spatial and Discrete Cosine Transform domains have been extracted to recognize the resampling operation. The spatial domain gives the information for the distribution of the pixels and DCT gives the edge information. Further, these Markov features are consolidated. Due to high dimensionality hard thresholding technique is used for reducing the dimensionality. Then, these Markov features are applied to the set of models of different classifiers. With the utilization of classifiers, weighted majority voting values have been calculated during the ensemble classification. Unlike the other techniques, these weighted voting boundaries have been consequently balanced during the training process until the best accuracy has been obtained. However, it is very difficult to get best accuracy so for getting best accuracy this research needs to do lots of iterations and trained the dataset. For the comparative study very few research has been found for this resampling forgery technique with different interpolation techniques and classifier. Still, comparison has been done with some latest research work. The comparative analysis shows that the proposed ensemble learning-based algorithm provides the best outcomes with the accuracy of 99.12% for bicubic, 98.89% for bilinear, and 98.23% for lanczos3 kernel with considerably less complexity and high speed in comparison to prior techniques which are using single support vector machine for classification. Moreover, the proposed algorithm also detects a very low probability of error of 0.44% and detects the type of interpolation kernel, size of the forgery, and the type of resampling, whether it is up sampling and down sampling, using Graphical User Interface which has not been detected previously with multiple forgery detection.

ESCRT-dependent control of craniofacial morphogenesis with concomitant perturbation of NOTCH signaling

Craniofacial development is orchestrated by transcription factor-driven regulatory networks, epigenetic modifications, and signaling pathways. Signaling molecules and their receptors rely on endo-lysosomal trafficking to prevent accumulation on the plasma membrane. ESCRT (Endosomal Sorting Complexes Required for Transport) machinery is recruited to endosomal membranes enabling degradation of such endosomal cargoes. Studies in vitro and in invertebrate models established the requirements of the ESCRT machinery in membrane remodeling, endosomal trafficking, and lysosomal degradation of activated membrane receptors. However, investigations during vertebrate development have been scarce. By ENU-induced mutagenesis, we isolated a mouse line, Vps25ENU/ENU, carrying a hypomorphic allele of the ESCRT-II component Vps25, with craniofacial anomalies resembling features of human congenital syndromes. Here, we assessed the spatiotemporal dynamics of Vps25 and additional ESCRT-encoding genes during murine development. We show that these genes are ubiquitously expressed although enriched in discrete domains of the craniofacial complex, heart, and limbs. ESCRT-encoding genes, including Vps25, are expressed in both cranial neural crest-derived mesenchyme and epithelium. Unlike constitutive ESCRT mutants, Vps25ENU/ENU embryos display late lethality. They exhibit hypoplastic lower jaw, stunted snout, dysmorphic ear pinnae, and secondary palate clefting. Thus, we provide the first evidence for critical roles of ESCRT-II in craniofacial morphogenesis and report perturbation of NOTCH signaling in craniofacial domains of Vps25ENU/ENU embryos. Given the known roles of NOTCH signaling in the developing cranium, and notably the lower jaw, we propose that the NOTCH pathway partly mediates the craniofacial defects of Vps25ENU/ENU mouse embryos.