Large gap asymptotics on annuli in the random normal matrix model.

We consider a two-dimensional determinantal point process arising in the random normal matrix model and which is a two-parameter generalization of the complex Ginibre point process. In this paper, we prove that the probability that no points lie on any number of annuli centered at 0 satisfies large n asymptotics of the form exp(C1n2+C2nlogn+C3n+C4n+C5logn+C6+Fn+O(n-112)),where n is the number of points of the process. We determine the constants C1,…,C6 explicitly, as well as the oscillatory term Fn which is of order 1. We also allow one annulus to be a disk, and one annulus to be unbounded. For the complex Ginibre point process, we improve on the best known results: (i) when the hole region is a disk, only C1,…,C4 were previously known, (ii) when the hole region is an unbounded annulus, only C1,C2,C3 were previously known, and (iii) when the hole region is a regular annulus in the bulk, only C1 was previously known. For general values of our parameters, even C1 is new. A main discovery of this work is that Fn is given in terms of the Jacobi theta function. As far as we know this is the first time this function appears in a large gap problem of a two-dimensional point process.

A hybrid stochastic interpolation and compression method for kernel matrices.

Kernel functions play an important role in a wide range of scientific computing and machine learning problems. These functions lead to dense kernel matrices that impose great challenges in computational costs at large scale. In this paper, we develop a set of fast kernel matrix compressing algorithms, which can reduce computation cost of matrix operations in the related applications. The foundation of these algorithms is the polyharmonic spline interpolation, which includes a set of radial basis functions that allow flexible choices of interpolating nodes, and a set of polynomial basis functions that guarantee the solvability and convergence of the interpolation. With these properties, original data points in the interacting kernel function can be randomly sampled with great flexibility, so the proposed method is suitable for complicated data structures, such as high-dimensionality, random distribution, or manifold. To further boost the algorithm accuracy and efficiency, this scheme is equipped with a QR sampling strategy, and combined with a recently developed fast stochastic SVD to form a hybrid method. If the overall number of degree of freedom is N, then the compressing algorithm has complexity of O(N) for low-rank matrices, and O(NlogN) for general matrices with a hierarchical structure. Numerical results for data on various domains and different kernel functions validate the accuracy and efficiency of the proposed method.

The general class of Wasserstein Sobolev spaces: density of cylinder functions, reflexivity, uniform convexity and Clarkson's inequalities.

We show that the algebra of cylinder functions in the Wasserstein Sobolev space H1,q(Pp(X,d),Wp,d,m) generated by a finite and positive Borel measure m on the (p,d)-Wasserstein space (Pp(X,d),Wp,d) on a complete and separable metric space (X,d) is dense in energy. As an application, we prove that, in case the underlying metric space is a separable Banach space B, then the Wasserstein Sobolev space is reflexive (resp. uniformly convex) if B is reflexive (resp. if the dual of B is uniformly convex). Finally, we also provide sufficient conditions for the validity of Clarkson's type inequalities in the Wasserstein Sobolev space.

Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics.

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the material is highly nonlinear in nature, as is common in biological tissue. In this work, we identify unknown material properties in continuum solid mechanics via physics-informed neural networks (PINNs). To improve the accuracy and efficiency of PINNs, we develop efficient strategies to nonuniformly sample observational data. We also investigate different approaches to enforce Dirichlet-type boundary conditions (BCs) as soft or hard constraints. Finally, we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space. The estimated material parameters achieve relative errors of less than 1%. As such, this work is relevant to diverse applications, including optimizing structural integrity and developing novel materials.

Free boundary dimers: random walk representation and scaling limit.

We study the dimer model on subgraphs of the square lattice in which vertices on a prescribed part of the boundary (the free boundary) are possibly unmatched. Each such unmatched vertex is called a monomer and contributes a fixed multiplicative weight z>0 to the total weight of the configuration. A bijection described by Giuliani et al. (J Stat Phys 163(2):211-238, 2016) relates this model to a standard dimer model but on a non-bipartite graph. The Kasteleyn matrix of this dimer model describes a walk with transition weights that are negative along the free boundary. Yet under certain assumptions, which are in particular satisfied in the infinite volume limit in the upper half-plane, we prove an effective, true random walk representation for the inverse Kasteleyn matrix. In this case we further show that, independently of the value of z>0, the scaling limit of the centered height function is the Gaussian free field with Neumann (or free) boundary conditions. It is the first example of a discrete model where such boundary conditions arise in the continuum scaling limit.

On singular values of large dimensional lag-τ sample auto-correlation matrices.

We study the limiting behavior of singular values of a lag-τ sample auto-correlation matrix Rτϵ of large dimensional vector white noise process, the error term ϵ in the high-dimensional factor model. We establish the limiting spectral distribution (LSD) that characterizes the global spectrum of Rτϵ, and derive the limit of its largest singular value. All the asymptotic results are derived under the high-dimensional asymptotic regime where the data dimension and sample size go to infinity proportionally. Under mild assumptions, we show that the LSD of Rτϵ is the same as that of the lag-τ sample auto-covariance matrix. Based on this asymptotic equivalence, we additionally show that the largest singular value of Rτϵ converges almost surely to the right end point of the support of its LSD. Based on these results, we further propose two estimators of total number of factors with lag-τ sample auto-correlation matrices in a factor model. Our theoretical results are fully supported by numerical experiments as well.

TRACY-WIDOM AT EACH EDGE OF REAL COVARIANCE AND MANOVA ESTIMATORS.

We study the sample covariance matrix for real-valued data with general population covariance, as well as MANOVA-type covariance estimators in variance components models under null hypotheses of global sphericity. In the limit as matrix dimensions increase proportionally, the asymptotic spectra of such estimators may have multiple disjoint intervals of support, possibly intersecting the negative half line. We show that the distribution of the extremal eigenvalue at each regular edge of the support has a GOE Tracy-Widom limit. Our proof extends a comparison argument of Ji Oon Lee and Kevin Schnelli, replacing a continuous Green function flow by a discrete Lindeberg swapping scheme.

The hyperfine magnetic fields and the effect of high pressure on the magnetic transition temperatures of the noncentrosymmetric FeRhGe2compound (B20).

Hyperfine parameters and the pressure dependence of the magnetic transition temperatures of FeRhGe2have been investigated. Sample has been prepared using high pressure-high temperature synthesis technique. FeRhGe2consists of two B20 structure phases with close lattice constants. The phase separation stays constant in the temperature range 4-300 K. The magnetic transition temperaturesTc1= 213 K andTc2= 135 K of FeRhGe2slightly increases with pressure in the range 0-4.5 GPa. We have compared this pressure dependence with some others compounds in the family Fe1-xRhxGe. The two phases in FeRhGe2have slightly different values of the hyperfine magnetic fields.

Complexity of linear relaxations in integer programming.

For a set X of integer points in a polyhedron, the smallest number of facets of any polyhedron whose set of integer points coincides with X is called the relaxation complexity  rc ( X ) . This parameter, introduced by Kaibel & Weltge (2015), captures the complexity of linear descriptions of X without using auxiliary variables. Using tools from combinatorics, geometry of numbers, and quantifier elimination, we make progress on several open questions regarding rc ( X ) and its variant rc Q ( X ) , restricting the descriptions of X to rational polyhedra. As our main results we show that rc ( X ) = rc Q ( X ) when: (a) X is at most four-dimensional, (b) X represents every residue class in ( Z / 2 Z ) d , (c) the convex hull of X contains an interior integer point, or (d) the lattice-width of X is above a certain threshold. Additionally, rc ( X ) can be algorithmically computed when X is at most three-dimensional, or X satisfies one of the conditions (b), (c), or (d) above. Moreover, we obtain an improved lower bound on rc ( X ) in terms of the dimension of X.

Central hubs prediction for bio networks by directed hypergraph - GA with validation to COVID-19 PPI.

Network structures have attracted much interest and have been rigorously studied in the past two decades. Researchers used many mathematical tools to represent these networks, and in recent days, hypergraphs play a vital role in this analysis. This paper presents an efficient technique to find the influential nodes using centrality measure of weighted directed hypergraph. Genetic Algorithm is exploited for tuning the weights of the node in the weighted directed hypergraph through which the characterization of the strength of the nodes, such as strong and weak ties by statistical measurements (mean, standard deviation, and quartiles) is identified effectively. Also, the proposed work is applied to various biological networks for identification of influential nodes and results shows the prominence the work over the existing measures. Furthermore, the technique has been applied to COVID-19 viral protein interactions. The proposed algorithm identified some critical human proteins that belong to the enzymes TMPRSS2, ACE2, and AT-II, which have a considerable role in hosting COVID-19 viral proteins and causes for various types of diseases. Hence these proteins can be targeted in drug design for an effective therapeutic against COVID-19.

Speed determinacy of travelling waves for a three-component lattice Lotka-Volterra competition system.

In this paper, the invasive speed selection of the monostable travelling wave for a three-component lattice Lotka-Volterra competition system is studied via the upper and lower solution method, as well as the comparison principle. By constructing several special upper and lower solutions, we establish sufficient conditions such that the linear or nonlinear selection is realized.

The bead process for beta ensembles.

The bead process introduced by Boutillier is a countable interlacing of the Sine 2 point processes. We construct the bead process for general Sine ß processes as an infinite dimensional Markov chain whose transition mechanism is explicitly described. We show that this process is the microscopic scaling limit in the bulk of the Hermite ß corner process introduced by Gorin and Shkolnikov, generalizing the process of the minors of the Gaussian Unitary and Orthogonal Ensembles. In order to prove our results, we use bounds on the variance of the point counting of the circular and the Gaussian beta ensembles, proven in a companion paper (Najnudel and Virág in Some estimates on the point counting of the Circular and the Gaussian Beta Ensemble, 2019).

Fluctuations of extreme eigenvalues of sparse Erdos-Rényi graphs.

We consider a class of sparse random matrices which includes the adjacency matrix of the Erdos-Rényi graph G ( N , p ) . We show that if N ε ⩽ N p ⩽ N 1 / 3 - ε then all nontrivial eigenvalues away from 0 have asymptotically Gaussian fluctuations. These fluctuations are governed by a single random variable, which has the interpretation of the total degree of the graph. This extends the result (Huang et al. in Ann Prob 48:916-962, 2020) on the fluctuations of the extreme eigenvalues from N p ⩾ N 2 / 9 + ε down to the optimal scale N p ⩾ N ε . The main technical achievement of our proof is a rigidity bound of accuracy N - 1 / 2 - ε ( N p ) - 1 / 2 for the extreme eigenvalues, which avoids the ( N p ) - 1 -expansions from Erdos et al. (Ann Prob 41:2279-2375, 2013), Huang et al. (2020) and Lee and Schnelli (Prob Theor Rel Fields 171:543-616, 2018). Our result is the last missing piece, added to Erdos et al. (Commun Math Phys 314:587-640, 2012), He (Bulk eigenvalue fluctuations of sparse random matrices. arXiv:1904.07140), Huang et al. (2020) and Lee and Schnelli (2018), of a complete description of the eigenvalue fluctuations of sparse random matrices for N p ⩾ N ε .

Large gap asymptotics for the generating function of the sine point process.

We consider the generating function of the sine point process on m consecutive intervals. It can be written as a Fredholm determinant with discontinuities, or equivalently as the convergent series ∑ k 1 , … , k m ⩾ 0 P ∩ j = 1 m # { points in the jth interval } = k j ∏ j = 1 m s j k j , where s 1 , … , s m ∈ [ 0 , + ∞ ) . In particular, we can deduce from it joint probabilities of the counting function of the process. In this work, we obtain large gap asymptotics for the generating function, which are asymptotics as the size of the intervals grows. Our results are valid for an arbitrary integer m , in the cases where all the parameters s 1 , … , s m , except possibly one, are positive. This generalizes two known results: (1) a result of Basor and Widom, which corresponds to m = 1 and s 1 > 0 , and (2) the case m = 1 and s 1 = 0 for which many authors have contributed. We also present some applications in the context of thinning and conditioning of the sine process.

Locating and Quantifying Carbon Steel Corrosion Rates Linked to Fungal B20 Biodiesel Degradation.

Fungi that degrade B20 biodiesel in storage tanks have also been linked to microbiologically influenced corrosion (MIC). A member of the filamentous fungal genus Paecilomyces and a yeast from the genus Wickerhamomyces were isolated from heavily contaminated B20 storage tanks from multiple Air Force bases. Although these taxa were linked to microbiologically influenced corrosion in situ, precise measurement of their corrosion rates and pitting severity on carbon steel was not available. In the experiments described here, we directly link fungal growth on B20 biodiesel to higher corrosion rates and pitting corrosion of carbon steel under controlled conditions. When these fungi were growing solely on B20 biodiesel for carbon and energy, consumption of FAME and n-alkanes was observed. The corrosion rates for both fungi were highest at the interface between the B20 biodiesel and the aqueous medium, where they acidified the medium and produced deeper pits than abiotic controls. Paecilomyces produced the most corrosion of carbon steel and produced the greatest pitting damage. This study characterizes and quantifies the corrosion of carbon steel by fungi that are common in fouled B20 biodiesel through their metabolism of the fuel, providing valuable insight for assessing MIC associated with storing and dispensing B20 biodiesel. IMPORTANCE Biodiesel is widely used across the United States and worldwide, blended with ultra-low-sulfur diesel in various concentrations. In this study, we were able to demonstrate that the filamentous fungus Paecilomyces AF001 and the yeast Wickerhamomyces SE3 were able to degrade fatty acid methyl esters and alkanes in biodiesel, causing increases in acidity. Both fungi also accelerated the corrosion of carbon steel, especially at the interface of the fuel and water, where their biofilms were located. This research provides controlled, quantified measurements and the localization of microbiologically influenced corrosion caused by common fungal contaminants in biodiesel fuels.

Generic and specific recurrent neural network models: Applications for large and small scale biopharmaceutical upstream processes.

The calculation of temporally varying upstream process outcomes is a challenging task. Over the last years, several parametric, semi-parametric as well as non-parametric approaches were developed to provide reliable estimates for key process parameters. We present generic and product-specific recurrent neural network (RNN) models for the computation and study of growth and metabolite-related upstream process parameters as well as their temporal evolution. Our approach can be used for the control and study of single product-specific large-scale manufacturing runs as well as generic small-scale evaluations for combined processes and products at development stage. The computational results for the product titer as well as various major upstream outcomes in addition to relevant process parameters show a high degree of accuracy when compared to experimental data and, accordingly, a reasonable predictive capability of the RNN models. The calculated values for the root-mean squared errors of prediction are significantly smaller than the experimental standard deviation for the considered process run ensembles, which highlights the broad applicability of our approach. As a specific benefit for platform processes, the generic RNN model is also used to simulate process outcomes for different temperatures in good agreement with experimental results. The high level of accuracy and the straightforward usage of the approach without sophisticated parameterization and recalibration procedures highlight the benefits of the RNN models, which can be regarded as promising alternatives to existing parametric and semi-parametric methods.

Dissemination of IncF group F1:A2:B20 plasmid-harbouring multidrug-resistant Escherichia coli ST131 before the acquisition of blaCTX-M in Japan.

OBJECTIVES: The Escherichia coli O25-ST131 clone is responsible for global dissemination of the blaCTX-M gene. However, the prevalence of this clone in the digestive tract, devoid of antimicrobial selection, and its molecular epidemiology remain unclear. In this study, we examined the origin of blaCTX-M-positive E. coli O25-ST131 and its distribution. METHODS: We separately sequenced the chromosomal and plasmid genomes of 50 E. coli O25 isolates obtained from faecal samples of patients with diarrhoea in Japan. RESULTS: Although 36 (72%) of 50 E. coli O25 isolates were ST131, only 6 harboured blaCTX-M. According to the fimH and ybbW sequences and fluoroquinolone susceptibility, H30R1 isolates were dominant (27/36; 75%) and possessed IncFII-FIA-FIB with FAB formula subtype F1:A2:B20 plasmids at a high frequency (24/27; 89%). The F1:A2:B20 plasmids possessed more resistance genes such as blaTEM-1, aminoglycoside resistance genes and trimethoprim/sulfamethoxazole resistance genes compared with non-F1:A2:B20 plasmids. In contrast, only one blaCTX-M-14 gene was located on the F1:A2:B20 plasmids, whereas the other three were located on IncFII (F4:A-:B-) (n = 1) and IncZ (n = 2) plasmids. Two H30Rx-ST131 isolates harboured blaCTX-M-15: one was on the chromosome and the other on the IncFIA-R plasmid. The stability and conjugation ability of the F1:A2:B20 plasmids were compared with those of non-F1:A2:B20 plasmids, which revealed higher stability but lower conjugative ability. CONCLUSIONS: These results suggest that E. coli H30R1-ST131 is a multidrug-resistant clone containing several resistance genes in the F1:A2:B20 plasmid, which were widely distributed before the acquisition of blaCTX-M.

Bistable wave speed of the Lotka-Volterra competition model.

This work deals with the speed sign of travelling waves to the Lotka-Volterra model with diffusion and bistable nonlinearity. We obtain new conditions for the determinacy of the sign of the bistable wave speed by constructing upper or lower solutions with an inside parameter to be adjusted. The established conditions improve or supplement the results in the references and give insight into the combined effect of system parameters on the propagation direction of the bistable wave.

Characterization of blaCTX-M-27/F1:A2:B20 Plasmids Harbored by Escherichia coli Sequence Type 131 Sublineage C1/H30R Isolates Spreading among Elderly Japanese in Nonacute-Care Settings.

We characterized 29 blaCTX-M-27-harboring plasmids of Escherichia coli sequence type 131 (ST131) sublineage C1/H30R isolates from healthy individuals and long-term-care facility (LTCF) residents. Most (27/29) plasmids were of the FIA, FIB, and FII multireplicon type with the same plasmid multilocus sequence typing (pMLST). Several plasmids (7/23) from LTCF residents harbored only blaCTX-M-27 as the resistance gene; however, their fundamental structures were very similar to those of previously isolated blaCTX-M-27/F1:A2:B20 plasmids, suggesting their prevalence as a newly arising public health concern.

In situ Linkage of Fungal and Bacterial Proliferation to Microbiologically Influenced Corrosion in B20 Biodiesel Storage Tanks.

Renewable fuels hold great promise for the future yet their susceptibility to biodegradation and subsequent corrosion represents a challenge that needs to be directly assessed. Biodiesel is a renewable fuel that is widely used as a substitute or extender for petroleum diesel and is composed of a mixture of fatty acid methyl esters derived from plant or animal fats. Biodiesel can be blended up to 20% v/v with ultra-low sulfur diesel (i.e., B20) and used interchangeably with diesel engines and infrastructure. The addition of biodiesel, however, has been linked to increased susceptibility to biodegradation. Microorganisms proliferating via degradation of biodiesel blends have been linked to microbiologically influenced corrosion in the laboratory, but not measured directly in storage tanks (i.e., in situ). To measure in situ microbial proliferation, fuel degradation and microbially influenced corrosion, we conducted a yearlong study of B20 storage tanks in operation at two locations, identified the microorganisms associated with fuel fouling, and measured in situ corrosion. The bacterial populations were more diverse than the fungal populations, and largely unique to each location. The bacterial populations included members of the Acetobacteraceae, Clostridiaceae, and Proteobacteria. The abundant Eukaryotes at both locations consisted of the same taxa, including a filamentous fungus within the family Trichocomaceae, not yet widely recognized as a contaminant of petroleum fuels, and the Saccharomycetaceae family of yeasts. Increases in the absolute and relative abundances of the Trichocomaceae were correlated with significant, visible fouling and pitting corrosion. This study identified the relationship between fouling of B20 with increased rates of corrosion and the microorganisms responsible, largely at the bottom of the sampled storage tanks. To our knowledge this is the first in situ study of this scale incorporating community and corrosion measurements in an active biodiesel storage environment.