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In this paper, we construct a number of 4-GDDs where the group sizes are all congruent to 2 (mod 3). We also show that 4-GDDs of type 2t8s exist for all but a finite number of feasible values of s and t. The largest unknown case has type 24818 and has 152 points. A number of 4-GDDs with at most 50 points are also constructed. These include one of type 4811101, the last feasible type of the form 4s1tn1 with at most 50 points for which no 4-GDD was known.

In optical see-through augmented reality (AR), information is often distributed between real and virtual contexts, and often appears at different distances from the user. To integrate information, users must repeatedly switch context and change focal distance. If the user’s task is conducted under time pressure, they may attempt to integrate information while their eye is still changing focal distance, a phenomenon we term transient focal blur. Previously, Gabbard, Mehra, and Swan (2018) examined these issues, using a text-based visual search task on a one-eye optical see-through AR display. This paper reports an experiment that partially replicates and extends this task on a custom-built AR Haploscope. The experiment examined the effects of context switching, focal switching distance, binocular and monocular viewing, and transient focal blur on task performance and eye fatigue. Context switching increased eye fatigue but did not decrease performance. Increasing focal switching distance increased eye fatigue and decreased performance. Monocular viewing also increased eye fatigue and decreased performance. The transient focal blur effect resulted in additional performance decrements, and is an addition to knowledge about AR user interface design issues.

Traditional combat models, such as Lanchester's equations, are typically limited to two competing populations and exhibit solutions characterized by exponential decay - and growth if logistics are included. We enrich such models to account for modern and future complexities, particularly around the role of interagency engagement in operations as often displayed in counterinsurgency operations. To address this, we explore incorporation of nontrophic effects from ecological modeling. This provides a global representation of asymmetrical combat between two forces in the modern setting in which noncombatant populations are present. As an example, we set the noncombatant population in our model to be a neutral agency supporting the native population to the extent that they are noncombatants. Correspondingly, the opposing intervention force is under obligations to enable an environment in which the neutral agency may undertake its work. In contrast to the typical behavior seen in the classic Lanchester system, our model gives rise to limit cycles and bifurcations that we interpret through a warfighting application. Finally, through a case study, we highlight the importance of the agility of a force in achieving victory when noncombatant populations are present.

A graph G is Ramsey for a graph H if every 2-coloring of the edges of G contains a monochromatic copy of H. We consider the following question: If H has bounded treewidth, is there a sparse graph G that is Ramsey for H? Two notions of sparsity are considered. Firstly, we show that if the maximum degree and treewidth of H are bounded, then there is a graph G with O(| V (H)| ) edges that is Ramsey for H. This was previously only known for the smaller class of graphs H with bounded bandwidth. On the other hand, we prove that in general the treewidth of a graph G that is Ramsey for H cannot be bounded in terms of the treewidth of H alone. In fact, the latter statement is true even if the treewidth is replaced by the degeneracy and H is a tree.

Canonical parametrisations of classical confocal coordinate systems are introduced and exploited to construct non-planar analogues of incircular (IC) nets on individual quadrics and systems of confocal quadrics. Intimate connections with classical deformations of quadrics that are isometric along asymptotic lines and circular cross-sections of quadrics are revealed. The existence of octahedral webs of surfaces of Blaschke type generated by asymptotic and characteristic lines that are diagonally related to lines of curvature is proved theoretically and established constructively. Appropriate samplings (grids) of these webs lead to three-dimensional extensions of non-planar IC nets. Three-dimensional octahedral grids composed of planes and spatially extending (checkerboard) IC-nets are shown to arise in connection with systems of confocal quadrics in Minkowski space. In this context, the Laguerre geometric notion of conical octahedral grids of planes is introduced. The latter generalise the octahedral grids derived from systems of confocal quadrics in Minkowski space. An explicit construction of conical octahedral grids is presented. The results are accompanied by various illustrations which are based on the explicit formulae provided by the theory.

An r-uniform hypergraph H consists of a set of vertices V and a set of edges whose elements are r-subsets of V. We define a hypertree to be a connected hypergraph which contains no cycles. A hypertree spans a hypergraph H if it is a subhypergraph of H which contains all vertices of H. Greenhill et al. (2017) gave an asymptotic formula for the average number of spanning trees in graphs with given, sparse degree sequence. We prove an analogous result for r-uniform hypergraphs with given degree sequence k=(k1,…,kn). Our formula holds when r5kmax3=o((kr−k−r)n), where k is the average degree and kmax is the maximum degree.

There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a rejection sampling algorithm for sampling simple uniform hypergraphs with a given degree sequence. Our algorithm uses, as a black box, an algorithm A for sampling bipartite graphs with given degrees, uniformly or nearly uniformly, in (expected) polynomial time. The expected runtime of the hypergraph sampling algorithm depends on the (expected) runtime of the bipartite graph sampling algorithm A, and the probability that a uniformly random bipartite graph with given degrees corresponds to a simple hypergraph. We give some conditions on the hypergraph degree sequence which guarantee that this probability is bounded below by a positive constant.

Hepatitis E virus (HEV) is one of the most common causes of acute viral hepatitis, mainly transmitted by fecal-oral route but has also been linked to fulminant hepatic failure, chronic hepatitis, and extrahepatic neurological and renal diseases. HEV is an emerging zoonotic pathogen with a broad host range, and strains of HEV from numerous animal species are known to cross species barriers and infect humans. HEV is a single-stranded, positive-sense RNA virus in the family Hepeviridae. The genome typically contains three open reading frames (ORFs): ORF1 encodes a nonstructural polyprotein for virus replication and transcription, ORF2 encodes the capsid protein that elicits neutralizing antibodies, and ORF3, which partially overlaps ORF2, encodes a multifunctional protein involved in virion morphogenesis and pathogenesis. HEV virions are non-enveloped spherical particles in feces but exist as quasi-enveloped particles in circulating blood. Two types of HEV virus-like particles (VLPs), small T = 1 (270 Å) and native virion-sized T = 3 (320–340 Å) have been reported. There exist two distinct forms of capsid protein, the secreted form (ORF2S) inhibits antibody neutralization, whereas the capsid-associated form (ORF2C) self-assembles to VLPs. Four cis-reactive elements (CREs) containing stem-loops from secondary RNA structures have been identified in the non-coding regions and are critical for virus replication. This mini-review discusses the current knowledge and gaps regarding the structural and molecular biology of HEV with emphasis on the virion structure, genomic organization, secondary RNA structures, viral proteins and their functions, and life cycle of HEV.

Hepatitis E virus (HEV) is one of the most common causes of acute viral hepatitis, mainly transmitted by fecal-oral route but has also been linked to fulminant hepatic failure, chronic hepatitis, and extrahepatic neurological and renal diseases. HEV is an emerging zoonotic pathogen with a broad host range, and strains of HEV from numerous animal species are known to cross species barriers and infect humans. HEV is a single-stranded, positive-sense RNA virus in the family Hepeviridae. The genome typically contains three open reading frames (ORFs): ORF1 encodes a nonstructural polyprotein for virus replication and transcription, ORF2 encodes the capsid protein that elicits neutralizing antibodies, and ORF3, which partially overlaps ORF2, encodes a multifunctional protein involved in virion morphogenesis and pathogenesis. HEV virions are non-enveloped spherical particles in feces but exist as quasi-enveloped particles in circulating blood. Two types of HEV virus-like particles (VLPs), small T = 1 (270 Å) and native virion-sized T = 3 (320–340 Å) have been reported. There exist two distinct forms of capsid protein, the secreted form (ORF2S) inhibits antibody neutralization, whereas the capsid-associated form (ORF2C) self-assembles to VLPs. Four cis-reactive elements (CREs) containing stem-loops from secondary RNA structures have been identified in the non-coding regions and are critical for virus replication. This mini-review discusses the current knowledge and gaps regarding the structural and molecular biology of HEV with emphasis on the virion structure, genomic organization, secondary RNA structures, viral proteins and their functions, and life cycle of HEV.

Hepatitis E virus (HEV) is one of the most common causes of acute viral hepatitis, mainly transmitted by fecal-oral route but has also been linked to fulminant hepatic failure, chronic hepatitis, and extrahepatic neurological and renal diseases. HEV is an emerging zoonotic pathogen with a broad host range, and strains of HEV from numerous animal species are known to cross species barriers and infect humans. HEV is a single-stranded, positive-sense RNA virus in the family Hepeviridae. The genome typically contains three open reading frames (ORFs): ORF1 encodes a nonstructural polyprotein for virus replication and transcription, ORF2 encodes the capsid protein that elicits neutralizing antibodies, and ORF3, which partially overlaps ORF2, encodes a multifunctional protein involved in virion morphogenesis and pathogenesis. HEV virions are non-enveloped spherical particles in feces but exist as quasi-enveloped particles in circulating blood. Two types of HEV virus-like particles (VLPs), small T = 1 (270 Å) and native virion-sized T = 3 (320–340 Å) have been reported. There exist two distinct forms of capsid protein, the secreted form (ORF2S) inhibits antibody neutralization, whereas the capsid-associated form (ORF2C) self-assembles to VLPs. Four cis-reactive elements (CREs) containing stem-loops from secondary RNA structures have been identified in the non-coding regions and are critical for virus replication. This mini-review discusses the current knowledge and gaps regarding the structural and molecular biology of HEV with emphasis on the virion structure, genomic organization, secondary RNA structures, viral proteins and their functions, and life cycle of HEV.

Hepatitis E virus (HEV) is one of the most common causes of acute viral hepatitis, mainly transmitted by fecal-oral route but has also been linked to fulminant hepatic failure, chronic hepatitis, and extrahepatic neurological and renal diseases. HEV is an emerging zoonotic pathogen with a broad host range, and strains of HEV from numerous animal species are known to cross species barriers and infect humans. HEV is a single-stranded, positive-sense RNA virus in the family Hepeviridae. The genome typically contains three open reading frames (ORFs): ORF1 encodes a nonstructural polyprotein for virus replication and transcription, ORF2 encodes the capsid protein that elicits neutralizing antibodies, and ORF3, which partially overlaps ORF2, encodes a multifunctional protein involved in virion morphogenesis and pathogenesis. HEV virions are non-enveloped spherical particles in feces but exist as quasi-enveloped particles in circulating blood. Two types of HEV virus-like particles (VLPs), small T = 1 (270 Å) and native virion-sized T = 3 (320–340 Å) have been reported. There exist two distinct forms of capsid protein, the secreted form (ORF2S) inhibits antibody neutralization, whereas the capsid-associated form (ORF2C) self-assembles to VLPs. Four cis-reactive elements (CREs) containing stem-loops from secondary RNA structures have been identified in the non-coding regions and are critical for virus replication. This mini-review discusses the current knowledge and gaps regarding the structural and molecular biology of HEV with emphasis on the virion structure, genomic organization, secondary RNA structures, viral proteins and their functions, and life cycle of HEV.

Hepatitis E virus (HEV) is one of the most common causes of acute viral hepatitis, mainly transmitted by fecal-oral route but has also been linked to fulminant hepatic failure, chronic hepatitis, and extrahepatic neurological and renal diseases. HEV is an emerging zoonotic pathogen with a broad host range, and strains of HEV from numerous animal species are known to cross species barriers and infect humans. HEV is a single-stranded, positive-sense RNA virus in the family Hepeviridae. The genome typically contains three open reading frames (ORFs): ORF1 encodes a nonstructural polyprotein for virus replication and transcription, ORF2 encodes the capsid protein that elicits neutralizing antibodies, and ORF3, which partially overlaps ORF2, encodes a multifunctional protein involved in virion morphogenesis and pathogenesis. HEV virions are non-enveloped spherical particles in feces but exist as quasi-enveloped particles in circulating blood. Two types of HEV virus-like particles (VLPs), small T = 1 (270 Å) and native virion-sized T = 3 (320–340 Å) have been reported. There exist two distinct forms of capsid protein, the secreted form (ORF2S) inhibits antibody neutralization, whereas the capsid-associated form (ORF2C) self-assembles to VLPs. Four cis-reactive elements (CREs) containing stem-loops from secondary RNA structures have been identified in the non-coding regions and are critical for virus replication. This mini-review discusses the current knowledge and gaps regarding the structural and molecular biology of HEV with emphasis on the virion structure, genomic organization, secondary RNA structures, viral proteins and their functions, and life cycle of HEV.

Hepatitis E virus (HEV) is one of the most common causes of acute viral hepatitis, mainly transmitted by fecal-oral route but has also been linked to fulminant hepatic failure, chronic hepatitis, and extrahepatic neurological and renal diseases. HEV is an emerging zoonotic pathogen with a broad host range, and strains of HEV from numerous animal species are known to cross species barriers and infect humans. HEV is a single-stranded, positive-sense RNA virus in the family Hepeviridae. The genome typically contains three open reading frames (ORFs): ORF1 encodes a nonstructural polyprotein for virus replication and transcription, ORF2 encodes the capsid protein that elicits neutralizing antibodies, and ORF3, which partially overlaps ORF2, encodes a multifunctional protein involved in virion morphogenesis and pathogenesis. HEV virions are non-enveloped spherical particles in feces but exist as quasi-enveloped particles in circulating blood. Two types of HEV virus-like particles (VLPs), small T = 1 (270 Å) and native virion-sized T = 3 (320–340 Å) have been reported. There exist two distinct forms of capsid protein, the secreted form (ORF2S) inhibits antibody neutralization, whereas the capsid-associated form (ORF2C) self-assembles to VLPs. Four cis-reactive elements (CREs) containing stem-loops from secondary RNA structures have been identified in the non-coding regions and are critical for virus replication. This mini-review discusses the current knowledge and gaps regarding the structural and molecular biology of HEV with emphasis on the virion structure, genomic organization, secondary RNA structures, viral proteins and their functions, and life cycle of HEV.

Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible semi-discretization in space, the class of problems under consideration is modeled by a system of ordinary differential equations where the right-hand side is a summation of two component functions, each corresponding to a given set of physical processes. The partitioned-exponential methods proposed herein evolve each component of the system via an exponential integrator, and information between partitions is exchanged via coupling terms. The traditional approach to constructing exponential methods, based on the variation-of-constants formula, is not directly applicable to partitioned systems. Rather, our approach to developing new partitioned-exponential families is based on a general-structure additive formulation of the schemes. Two method formulations are considered, one based on a linear-nonlinear splitting of the right hand component functions, and another based on approximate Jacobians. The paper develops classical (non-stiff) order conditions theory for partitioned exponential schemes based on particular families of T-trees and B-series theory. Several practical methods of third order are constructed that extend the Rosenbrock-type and EPIRK families of exponential integrators. Several implementation optimizations specific to the application of these methods to reaction-diffusion systems are also discussed. Numerical experiments reveal that the new partitioned-exponential methods can perform better than traditional unpartitioned exponential methods on some problems.

Systems driven by multiple physical processes are central to many areas of science and engineering. Time discretization of multiphysics systems is challenging, since different processes have different levels of stiffness and characteristic time scales. The multimethod approach discretizes each physical process with an appropriate numerical method; the methods are coupled appropriately such that the overall solution has the desired accuracy and stability properties. The authors developed the general-structure additive Runge–Kutta (GARK) framework, which constructs multimethods based on Runge–Kutta schemes. This paper constructs the new GARK-ROS/GARK-ROW families of multimethods based on linearly implicit Rosenbrock/Rosenbrock-W schemes. For ordinary differential equation models, we develop a general order condition theory for linearly implicit methods with any number of partitions, using exact or approximate Jacobians. We generalize the order condition theory to two-way partitioned index-1 differential-algebraic equations. Applications of the framework include decoupled linearly implicit, linearly implicit/explicit, and linearly implicit/implicit methods. Practical GARK-ROS and GARK-ROW schemes of order up to four are constructed.

In this paper, we derive (partial) convex hull for deterministic multi-constraint polyhedral conic mixed integer sets with multiple integer variables using conic mixed integer rounding (CMIR) cut-generation procedure of Atamtürk and Narayanan (Math Prog 122:1–20, 2008), thereby extending their result for a simple polyhedral conic mixed integer set with single constraint and one integer variable. We then introduce two-stage stochastic p-order conic mixed integer programs (denoted by TSS-CMIPs) in which the second stage problems have sum of lp-norms in the objective function along with integer variables. First, we present sufficient conditions under which the addition of scenario-based nonlinear cuts in the extensive formulation of TSS-CMIPs is sufficient to relax the integrality restrictions on the second stage integer variables without impacting the integrality of the optimal solution of the TSS-CMIP. We utilize scenario-based CMIR cuts for TSS-CMIPs and their distributionally robust generalizations with structured CMIPs in the second stage, and prove that these cuts provide conic/linear programming equivalent or approximation for the second stage CMIPs. We also perform extensive computational experiments by solving stochastic and distributionally robust capacitated facility location problem and randomly generated structured TSS-CMIPs with polyhedral CMIPs and second-order CMIPs in the second stage, i.e. p= 1 and p= 2 , respectively. We observe that there is a significant reduction in the total time taken to solve these problems after adding the scenario-based cuts.

Complex numerical weather prediction models incorporate a variety of physical processes, each described by multiple alternative physical schemes with specific parameters. The selection of the physical schemes and the choice of the corresponding physical parameters during model configuration can significantly impact the accuracy of model forecasts. There is no combination of physical schemes that works best for all times, at all locations, and under all conditions. It is therefore of considerable interest to understand the interplay between the choice of physics and the accuracy of the resulting forecasts under different conditions. This paper demonstrates the use of machine learning techniques to study the uncertainty in numerical weather prediction models due to the interaction of multiple physical processes. The first problem addressed herein is the estimation of systematic model errors in output quantities of interest at future times, and the use of this information to improve the model forecasts. The second problem considered is the identification of those specific physical processes that contribute most to the forecast uncertainty in the quantity of interest under specified meteorological conditions. In order to address these questions we employ two machine learning approaches, random forests and artificial neural networks. The discrepancies between model results and observations at past times are used to learn the relationships between the choice of physical processes and the resulting forecast errors. Numerical experiments are carried out with the Weather Research and Forecasting (WRF) model. The output quantity of interest is the model precipitation, a variable that is both extremely important and very challenging to forecast. The physical processes under consideration include various micro-physics schemes, cumulus parameterizations, short wave, and long wave radiation schemes. The experiments demonstrate the strong potential of machine learning approaches t

Consider a matrix M chosen uniformly at random from a class of m×n matrices of zeros and ones with prescribed row and column sums. A partially filled matrix D is a defining set for M if M is the unique member of its class that contains the entries in D. The size of a defining set is the number of filled entries. A critical set is a defining set for which the removal of any entry stops it being a defining set. For some small fixed ε>0, we assume that n⩽m=o(n1+ε), and that λ⩽1∕2, where λ is the proportion of entries of M that equal 1. We also assume that the row sums of M do not vary by more than O(n1∕2+ε), and that the column sums do not vary by more than O(m1∕2+ε). Under these assumptions we show that M almost surely has no defining set of size less than λmn−O(m7∕4+ε). It follows that M almost surely has no critical set of size more than (1−λ)mn+O(m7∕4+ε). Our results generalise a theorem of Cavenagh and Ramadurai, who examined the case when λ=1∕2 and n=m=2k for an integer k.

Vascular dementia (VaD) is a complex neurocognitive disorder secondary to a variety of cerebrovascular lesions. Numerous studies have shown that lipid metabolism is involved in the pathobiology of the disease. We examined the plasma lipid profiles in VaD, with the expectation of identifying reliable lipid biomarkers for VaD. 49 VaD patients and 48 healthy controls were recruited from Bankstown-Lidcombe Hospital in Sydney, Australia. Lipids were extracted by single phase 1-butanol/methanol, and untargeted analysis was performed by liquid chromatography coupled-mass spectrometry (LC–MS/MS). Univariate analysis of variance was used to examine the differences in lipid classes and individual lipids between VaD and control groups. In an independent sample of 161 subjects from the Older Australian Twins Study (OATS), elastic net penalization for the generalized linear model (Glmnet) and Random Forest were applied to the lipid levels to subcategorise the sample into vascular cognitive impairment and controls. Most lipids belonging to the classes of ceramides (Cer), cholesterol esters (ChE) and phospholipids were significantly lower in VaD plasma, while glycerides were elevated compared to controls. Levels of ChE, Cer and the two lipid classes together achieved the best accuracy in discriminating VaD from controls, with more than 80% accuracy. The probable VaD group in the OATS sample predicted by the lipid levels showed greater impairment in most cognitive domains, especially attention and processing speed and executive function from controls but did not differ in white matter hyperintensities and DTI measures. As a conclusion, plasma lipids levels, in particular Cer and ChE, are abnormal in VaD and may help discriminate them from healthy controls. Understanding the basis of these differences may provide insights into the pathobiology of VaD.

Single-cell mRNA sequencing has been adopted as a powerful technique for understanding gene expression profiles at the single-cell level. However, challenges remain due to factors such as the inefficiency of mRNA molecular capture, technical noises and separate sequencing of cells in different batches. Normalization methods have been developed to ensure a relatively accurate analysis. This work presents a survey on 10 tools specifically designed for single-cell mRNA sequencing data preprocessing steps, among which 6 tools are used for dropout normalization and 4 tools are for batch effect correction. In this survey, we outline the main methodology for each of these tools, and we also compare these tools to evaluate their normalization performance on datasets which are simulated under the constraints of dropout inefficiency, batch effect or their combined effects. We found that Saver and Baynorm performed better than other methods in dropout normalization, in most cases. Beer and Batchelor performed better in the batch effect normalization, and the Saver–Beer tool combination and the Baynorm–Beer combination performed better in the mixed dropout-and-batch effect normalization. Over-normalization is a common issue occurred to these dropout normalization tools that is worth of future investigation. For the batch normalization tools, the capability of retaining heterogeneity between different groups of cells after normalization can be another direction for future improvement

A frequency square is a matrix in which each row and column is a permutation of the same multiset of symbols. We consider only binary frequency squares of order n with n/2 zeros and n/2 ones in each row and column. Two such frequency squares are orthogonal if, when superimposed, each of the 4 possible ordered pairs of entries occurs equally often. In this context we say that a set of k-MOFS(n) is a set of k binary frequency squares of order n in which each pair of squares is orthogonal.

Particle Markov Chain Monte Carlo methods are used to carry out inference in nonlinear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform Bayesian inference using either a particle marginal Metropolis–Hastings (PMMH) algorithm or a particle Gibbs (PG) sampler. This paper shows how the two ways of generating variables mentioned above can be combined in a flexible manner to give sampling schemes that converge to a desired target distribution. The advantage of our approach is that the sampling scheme can be tailored to obtain good results for different applications. For example, when some parameters and the states are highly correlated, such parameters can be generated using PMMH, while all other parameters are generated using PG because it is easier to obtain good proposals for the parameters within the PG framework. We derive some convergence properties of our sampling scheme and also investigate its performance empirically by applying it to univariate and multivariate stochastic volatility models and comparing it to other PMCMC methods proposed in the literature.

We extend and provide new proofs of the Wei-type duality theorems, due to Ducoat and Ravagnani, for Gabidulin–Roth rank-metric codes and for Delsarte rank-metric codes. These results follow as corollaries from fundamental Wei-type duality theorems that we prove for certain general combinatorial structures.

The brain is a highly complex organ consisting of numerous types of cells with ample diversity at the epigenetic level to achieve distinct gene expression profiles. During neuronal cell specification, transcription factors (TFs) form regulatory modules with chromatin remodeling proteins to initiate the cascade of epigenetic changes. Currently, little is known about brain epigenetic regulatory modules and how they regulate gene expression in a cell-type specific manner. To infer TFs involved in neuronal specification, we applied a recursive motif search approach on the differentially methylated regions identified from single-cell methylomes. The epigenetic transcription regulatory modules (ETRM), including EGR1 and MEF2C, were predicted and the co-expression of TFs in ETRMs were examined with RNA-seq data from single or sorted brain cells using a conditional probability matrix. Lastly, computational predications were validated with EGR1 ChIP-seq data. In addition, methylome and RNA-seq data generated from Egr1 knockout mice supported the essential role of EGR1 in brain epigenome programming, in particular for excitatory neurons. In summary, we demonstrated that brain single cell methylome and RNA-seq data can be integrated to gain a better understanding of how ETRMs control cell specification. The analytical pipeline implemented in this study is freely accessible in the Github repository (https://github.com/Gavin-Yinld/brain_TF).

The brain is a highly complex organ consisting of numerous types of cells with ample diversity at the epigenetic level to achieve distinct gene expression profiles. During neuronal cell specification, transcription factors (TFs) form regulatory modules with chromatin remodeling proteins to initiate the cascade of epigenetic changes. Currently, little is known about brain epigenetic regulatory modules and how they regulate gene expression in a cell-type specific manner. To infer TFs involved in neuronal specification, we applied a recursive motif search approach on the differentially methylated regions identified from single-cell methylomes. The epigenetic transcription regulatory modules (ETRM), including EGR1 and MEF2C, were predicted and the co-expression of TFs in ETRMs were examined with RNA-seq data from single or sorted brain cells using a conditional probability matrix. Lastly, computational predications were validated with EGR1 ChIP-seq data. In addition, methylome and RNA-seq data generated from Egr1 knockout mice supported the essential role of EGR1 in brain epigenome programming, in particular for excitatory neurons. In summary, we demonstrated that brain single cell methylome and RNA-seq data can be integrated to gain a better understanding of how ETRMs control cell specification. The analytical pipeline implemented in this study is freely accessible in the Github repository (https://github.com/Gavin-Yinld/brain_TF).

The brain is a highly complex organ consisting of numerous types of cells with ample diversity at the epigenetic level to achieve distinct gene expression profiles. During neuronal cell specification, transcription factors (TFs) form regulatory modules with chromatin remodeling proteins to initiate the cascade of epigenetic changes. Currently, little is known about brain epigenetic regulatory modules and how they regulate gene expression in a cell-type specific manner. To infer TFs involved in neuronal specification, we applied a recursive motif search approach on the differentially methylated regions identified from single-cell methylomes. The epigenetic transcription regulatory modules (ETRM), including EGR1 and MEF2C, were predicted and the co-expression of TFs in ETRMs were examined with RNA-seq data from single or sorted brain cells using a conditional probability matrix. Lastly, computational predications were validated with EGR1 ChIP-seq data. In addition, methylome and RNA-seq data generated from Egr1 knockout mice supported the essential role of EGR1 in brain epigenome programming, in particular for excitatory neurons. In summary, we demonstrated that brain single cell methylome and RNA-seq data can be integrated to gain a better understanding of how ETRMs control cell specification. The analytical pipeline implemented in this study is freely accessible in the Github repository (https://github.com/Gavin-Yinld/brain_TF).

The brain is a highly complex organ consisting of numerous types of cells with ample diversity at the epigenetic level to achieve distinct gene expression profiles. During neuronal cell specification, transcription factors (TFs) form regulatory modules with chromatin remodeling proteins to initiate the cascade of epigenetic changes. Currently, little is known about brain epigenetic regulatory modules and how they regulate gene expression in a cell-type specific manner. To infer TFs involved in neuronal specification, we applied a recursive motif search approach on the differentially methylated regions identified from single-cell methylomes. The epigenetic transcription regulatory modules (ETRM), including EGR1 and MEF2C, were predicted and the co-expression of TFs in ETRMs were examined with RNA-seq data from single or sorted brain cells using a conditional probability matrix. Lastly, computational predications were validated with EGR1 ChIP-seq data. In addition, methylome and RNA-seq data generated from Egr1 knockout mice supported the essential role of EGR1 in brain epigenome programming, in particular for excitatory neurons. In summary, we demonstrated that brain single cell methylome and RNA-seq data can be integrated to gain a better understanding of how ETRMs control cell specification. The analytical pipeline implemented in this study is freely accessible in the Github repository (https://github.com/Gavin-Yinld/brain_TF).

The brain is a highly complex organ consisting of numerous types of cells with ample diversity at the epigenetic level to achieve distinct gene expression profiles. During neuronal cell specification, transcription factors (TFs) form regulatory modules with chromatin remodeling proteins to initiate the cascade of epigenetic changes. Currently, little is known about brain epigenetic regulatory modules and how they regulate gene expression in a cell-type specific manner. To infer TFs involved in neuronal specification, we applied a recursive motif search approach on the differentially methylated regions identified from single-cell methylomes. The epigenetic transcription regulatory modules (ETRM), including EGR1 and MEF2C, were predicted and the co-expression of TFs in ETRMs were examined with RNA-seq data from single or sorted brain cells using a conditional probability matrix. Lastly, computational predications were validated with EGR1 ChIP-seq data. In addition, methylome and RNA-seq data generated from Egr1 knockout mice supported the essential role of EGR1 in brain epigenome programming, in particular for excitatory neurons. In summary, we demonstrated that brain single cell methylome and RNA-seq data can be integrated to gain a better understanding of how ETRMs control cell specification. The analytical pipeline implemented in this study is freely accessible in the Github repository (https://github.com/Gavin-Yinld/brain_TF).

The brain is a highly complex organ consisting of numerous types of cells with ample diversity at the epigenetic level to achieve distinct gene expression profiles. During neuronal cell specification, transcription factors (TFs) form regulatory modules with chromatin remodeling proteins to initiate the cascade of epigenetic changes. Currently, little is known about brain epigenetic regulatory modules and how they regulate gene expression in a cell-type specific manner. To infer TFs involved in neuronal specification, we applied a recursive motif search approach on the differentially methylated regions identified from single-cell methylomes. The epigenetic transcription regulatory modules (ETRM), including EGR1 and MEF2C, were predicted and the co-expression of TFs in ETRMs were examined with RNA-seq data from single or sorted brain cells using a conditional probability matrix. Lastly, computational predications were validated with EGR1 ChIP-seq data. In addition, methylome and RNA-seq data generated from Egr1 knockout mice supported the essential role of EGR1 in brain epigenome programming, in particular for excitatory neurons. In summary, we demonstrated that brain single cell methylome and RNA-seq data can be integrated to gain a better understanding of how ETRMs control cell specification. The analytical pipeline implemented in this study is freely accessible in the Github repository (https://github.com/Gavin-Yinld/brain_TF).

In this paper, we evaluate a smoothed character sum involving$\sum_{m}\sum_{n}\leg {m}{n}$, with quadratic, cubic or quartic Heckecharacters $\leg {m}{n}$, and the two sums over $m$ and $n$ are of comparablelengths.

Suppose that $d \in \{ 2, 3, 4, 6 \}$ and $a \in \mathbb{Z}$ with $a\neq -1$and $a$ is not square. Let $P_{(a,d)}$ be the number of primes $p$ notexceeding $x$ such that $p \equiv 1 \pmod{d}$ and $a^{(p-1)/d} \equiv 1\pmod{p}$. In this paper, we study the mean value of $P_{(a,d)}$.

© The authors. Released under the CC BY-ND license (International 4.0). Let Hn be a graph on n vertices and let Hn denote the complement of Hn. Suppose that ∆ = ∆(n) is the maximum degree of Hn. We analyse three algorithms for sampling d-regular subgraphs (d-factors) of Hn. This is equivalent to uniformly sampling d-regular graphs which avoid a set E(Hn) of forbidden edges. Here d = d(n) is a positive integer which may depend on n. Two of these algorithms produce a uniformly random d-factor of Hn in expected runtime which is linear in n and low-degree polynomial in d and ∆. The first algorithm applies when (d + ∆)d∆ = o(n). This improves on an earlier algorithm by the first author, which required constant d and at most a linear number of edges in Hn. The second algorithm applies when Hn is regular and d2 + ∆2 = o(n), adapting an approach developed by the first author together with Wormald. The third algorithm is a simplification of the second, and produces an approximately uniform d-factor of Hn in time O(dn). Here the output distribution differs from uniform by o(1) in total variation distance, provided that d2 + ∆2 = o(n).

©© 2019 Society for Industrial and Applied Mathematics We consider the problem of q-coloring a k-uniform random hypergraph, where q, k > 3, and determine the rigidity threshold. For edge densities above the rigidity threshold, we show that almost all solutions have a linear number of vertices that are linearly frozen, meaning that they cannot be recolored by a sequence of colorings that each change the color of a sublinear number of vertices. When the edge density is below the threshold, we prove that all but a vanishing proportion of the vertices can be recolored by a sequence of colorings that recolor only one vertex at a time. This change in the geometry of the solution space has been hypothesized to be the cause of the algorithmic barrier faced by naive coloring algorithms. Our calculations verify predictions made by statistical physicists using the nonrigorous cavity method. The traditional model for problems of this type is the random coloring model, where a random hypergraph is chosen and then a random coloring of that hypergraph is selected. However, it is often easier to work with the planted model, where a random coloring is selected first, and then edges are randomly chosen which respect the coloring. As part of our analysis, we show that up to the condensation phase transition, the random coloring model is contiguous with respect to the planted model. This result is of independent interest.

Peer reviews, evaluations, and selections are a fundamental aspect of modern science. Funding bodies the world over employ experts to review and select the best proposals from those submitted for funding. The problem of peer selection, however, is much more general: a professional society may want to give a subset of its members awards based on the opinions of all members; an instructor for a Massive Open Online Course (MOOC) or an online course may want to crowdsource grading; or a marketing company may select ideas from group brainstorming sessions based on peer evaluation. We make three fundamental contributions to the study of peer selection, a specific type of group decision-making problem, studied in computer science, economics, and political science. First, we propose a novel mechanism that is strategyproof, i.e., agents cannot benefit by reporting insincere valuations. Second, we demonstrate the effectiveness of our mechanism by a comprehensive simulation-based comparison with a suite of mechanisms found in the literature. Finally, our mechanism employs a randomized rounding technique that is of independent interest, as it solves the apportionment problem that arises in various settings where discrete resources such as parliamentary representation slots need to be divided proportionally.

The particle swarm optimization (PSO) algorithm is a stochastic search technique based on the social dynamics of a flock of birds. It has been established that the performance of the PSO algorithm is sensitive to the values assigned to its control parameters. Many studies have examined the long-term behaviours of various PSO parameter configurations, but have failed to provide a quantitative analysis across a variety of benchmark problems. Furthermore, two important questions have remained unanswered. Specifically, the effects of the balance between the values of the acceleration coefficients on the optimal parameter regions, and whether the optimal parameters to employ are time-dependent, warrant further investigation. This study addresses both questions by examining the performance of a global-best PSO using 3036 different parameter configurations on a set of 22 benchmark problems. Results indicate that the balance between the acceleration coefficients does impact the regions of parameter space that lead to optimal performance. Additionally, this study provides concrete evidence that, for the examined problem dimensions, larger acceleration coefficients are preferred as the search progresses, thereby indicating that the optimal parameters are, in fact, time-dependent. Finally, this study provides a general recommendation for the selection of PSO control parameter values.

A fire code has been developed for the purpose of modelling wildland fires via Large Eddy Simulation (LES) and the use of the level-set approach to track the flame front. Detailed chemical kinetics have been considered via the strained laminar flamelet approach for the combustion process which included the consideration of the yields of toxic volatiles such as CO, CO2 and soot production. Numerical simulations have been validated against an experimental study on the fire spread on a pine needle board under different slope angles. Peak temperatures and occurrence times during the propagation process were predicted with an overall average error of 11% and 3% respectively. This demonstrates that the flaming behaviour could be well predicted under different slope conditions. By incorporating the level set with the gas phase models, information including temperature field, toxic volatiles and soot particle concentrations can be realised in comparison to empirical fire spread models.

© 2018 Elsevier B.V. The recent introduction of the renewal Hawkes (RHawkes) process has extended the modeling capabilities of the classical Hawkes self-exciting process by allowing the immigrant arrival times to follow a general renewal process rather than a homogeneous Poisson process. A multivariate extension to the RHawkes process will be proposed, which allows different event types to interact with self- and cross-excitation effects, termed the multivariate renewal Hawkes (MRHawkes) process model. A recursive algorithm is developed to directly compute the likelihood of the model, which forms the basis of statistical inference. A modified algorithm for likelihood evaluation is also proposed which reduces computational time. The likelihood evaluation algorithm also implies a procedure to assess the goodness-of-fit of the temporal patterns of the events and distribution of the event types by computing independent and uniform residuals. The plug-in predictive density function for the next event time and methods to make future predictions using simulations are presented. Simulation studies will show that the likelihood evaluation algorithms and the prediction procedures are performing as expected. To illustrate the proposed methodology, data on earthquakes arising in two Pacific island countries Fiji and Vanuatu and trade-through data for the stock BNP Paribas on the Euronext Paris stock exchange are analyzed.