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Nucleic acids such as mRNA have emerged as a promising therapeutic modality with the capability of addressing a wide range of diseases. Lipid nanoparticles (LNPs) as a delivery platform for nucleic acids were used in the COVID-19 vaccines and have received much attention. While modern manufacturing processes which involve rapidly mixing an organic stream containing the lipids with an aqueous stream containing the nucleic acids are conceptually straightforward, detailed understanding of LNP formation and structure is still limited and scale-up can be challenging. Mathematical and computational methods are a promising avenue for deepening scientific understanding of the LNP formation process and facilitating improved process development and control. This article describes strategies for the mechanistic modeling of LNP formation, starting with strategies to estimate and predict important physicochemical properties of the various species such as diffusivities and solubilities. Subsequently, a framework is outlined for constructing mechanistic models of reactor- and particle-scale processes. Insights gained from the various models are mapped back to product quality attributes and process insights. Lastly, the use of the models to guide development of advanced process control and optimization strategies is discussed., Comment: 67 pages, 10 figures

Many industries widely adopted hub networks these days. Managing logistics, transportation, and distribution requires a delicate balance to ensure seamless operations within this network. Hub network promotes cost-effective routing through inter-hub flows. Failure of such hubs may impact the total network with huge costs. In this paper, we study bilevel $q$-allocation hub interdiction problem. In previous literature hub interdiction problem was studied with single and multiple allocation protocols.This problem focus on $q$ allocation which solves single and multiple allocation problem as special case. We also show improvements on the branch and cut approach by using cutting planes.Our experiments based on large instances present the efficiency of the approach to solve some previously unsolved instances., Comment: There are some technical errors in the paper. The pareto section is not right and computational results are missing

This research examines the nonadiabatic dynamics of cyclobutanone after excitation into the n-3s Rydberg S2 state. It stems from our contribution to the Special Topic of the Journal of Chemical Physics to test the predictive capability of computational chemistry against unseen experimental data. Decoherence-corrected fewest-switches surface hopping (DC-FSSH) was used to simulate nonadiabatic dynamics with full and approximated nonadiabatic couplings. Several simulation sets were computed with different electronic structure methods, including a multiconfigurational wavefunction (MCSCF) specially built to describe dissociative channels, multireference semiempirical approach, time-dependent density functional theory, algebraic diagrammatic construction, and coupled cluster. MCSCF dynamics predicts a slow deactivation of the S2 state (10 ps), followed by an ultrafast population transfer from S1 to S0 (<100 fs). CO elimination (C3 channel) dominates C2H4 formation (C2 channel). These findings radically differ from the other methods, which predicted S2 lifetimes 10 to 250 times shorter and C2 channel predominance. These results suggest that routine electronic structure methods may hold low predictive power for the outcome of nonadiabatic dynamics., Comment: The main manuscript contains 28 pages with 8 figures. The supplementary material contains 14 pages with 12 figures. In total, the merged pdf document has 42 pages with 20 figures

One of the major impediments in deployment of Autonomous Driving Systems (ADS) is their safety and reliability. The primary reason for the complexity of testing ADS is that it operates in an open world characterized by its non-deterministic, high-dimensional and non-stationary nature where the actions of other actors in the environment are uncontrollable from the ADS's perspective. This leads to a state space explosion problem and one way of mitigating this problem is by concretizing the scope for the system under test (SUT) by testing for a set of behavioral competencies which an ADS must demonstrate. A popular approach to testing ADS is scenario-based testing where the ADS is presented with driving scenarios from real world (and synthetically generated) data and expected to meet defined safety criteria while navigating through the scenario. We present SAFR-AV, an end-to-end ADS testing platform to enable scenario-based ADS testing. Our work addresses key real-world challenges of building an efficient large scale data ingestion pipeline and search capability to identify scenarios of interest from real world data, creating digital twins of the real-world scenarios to enable Software-in-the-Loop (SIL) testing in ADS simulators and, identifying key scenario parameter distributions to enable optimization of scenario coverage. These along with other modules of SAFR-AV would allow the platform to provide ADS pre-certifications.

We study two properties for subsets of a metric space. One of them is generalization of chainability, finite chainability, and Menger convexity for metric spaces; while the other is a generalization of compactness. We explore the basic results related to these two properties. Further, in the perspective of these properties, we explore relations among the Hausdorff, Vietoris, and locally finite hypertopologies.

A generalization of the Lebesgue number lemma is obtained. It is proved that, if each countably infinite locally finite open cover of a chainable metric space $X$ has a Lebesgue number, then $X$ is totally bounded. A property of metric spaces which is a generalization of connectedness and Menger convexity is introduced. It is observed that Atsujiness and compactness are equivalent for a metric space with this introduced property as well as for a chainable metric space., Comment: 6

Given uniformly homeomorphic metric spaces $X$ and $Y$, it is proved that the hyperspaces $C(X)$ and $C(Y)$ are uniformly homeomorphic, where $C(X)$ denotes the collection of all nonempty closed subsets of $X$, and is endowed with Hausdorff distance. Gerald Beer has proved that the hyperspace $C(X)$ is Atsuji when $X$ is either compact or uniformly discrete. An Atsuji space is a generalization of compact metric spaces as well as of uniformly discrete spaces. In this article, we investigate the space $C(X)$ when $X$ is Atsuji, and a class of Atsuji subspaces of $C(X)$ is obtained. Using the obtained results, some fixed point results for continuous maps on Atsuji spaces are obtained., Comment: 9

Most knowledge graph use cases are data-centric, focusing on representing data entities and their semantic relationships. There are no published success stories to represent large-scale complicated business logic with knowledge graph technologies. In this paper, we will share our innovative and practical approach to representing complicated U.S. and Canadian income tax compliance logic (calculations and rules) via a large-scale knowledge graph. We will cover how the Tax Knowledge Graph is constructed and automated, how it is used to calculate tax refunds, reasoned to find missing info, and navigated to explain the calculated results. The Tax Knowledge Graph has helped transform Intuit's flagship TurboTax product into a smart and personalized experience, accelerating and automating the tax preparation process while instilling confidence for millions of customers., Comment: KDD2020 International Workshop on Knowledge Graph: Mining Knowledge Graph for Deep Insights. See: https://suitclub.ischool.utexas.edu/IWKG_KDD2020/index.html. 6 pages, 9 figures

Rotating spiral patterns in Rayleigh-B\'enard convection are known to induce azimuthal flows, which raises the question of how different neighboring spirals interact with each other in spiral chaos, and the role of hydrodynamics in this regime. Far from the core, we show that spiral rotations lead to an azimuthal body force that is irrotational and of magnitude proportional to the topological index of the spiral and its angular frequency. The force, although irrotational, cannot be included in the pressure field as it would lead to a nonphysical, multivalued pressure. We calculate the asymptotic dependence of the resulting flow, and show that it leads to a logarithmic dependence of the azimuthal velocity on distance r away from the spiral core in the limit of negligible damping coefficient. This solution dampens to approximately $1/r$ when accounting for no-slip boundary conditions for the convection cell's plate. This flow component can provide additional hydrodynamic interactions among spirals including those observed in spiral defect chaos. We show that the analytic prediction for the azimuthal velocity agrees with numerical results obtained from both two-dimensional generalized Swift-Hohenberg and three-dimensional Boussinesq models, and find that the velocity field is affected by the size and charges of neighboring spirals. Numerically, we identify a correlation between the appearance of spiral defect chaos and the balancing between the mean-flow advection and the diffusive dynamics related to roll unwinding.

In frame theory literature, there are several generalizations of frame, K-fusion frame presents a flavour of one such generalization, basically it is an intertwined replica of K-frame and fusion frame. K-fusion frames come naturally (having significant applications) when one needs to reconstruct functions (signals) from a large data in the range of a bounded linear operator. Getting inspiration from the concept of weaving frames in Hilbert space, we study the weaving form of K-fusion frames which have significant applications in wireless sensor networks. This article produces various characterizations of weaving K-fusion frames in different spaces. Furthermore, Paley-Wiener type perturbation and conditions on erasure of frame components have been assembled to scrutinize wovenness of the same., Comment: 9 pages. arXiv admin note: text overlap with arXiv:1907.08757

Shimizu and Takahashi have shown that every decreasing sequence of nonempty, bounded, closed, convex subsets of a complete, uniformly Takahashi convex metric space has nonempty intersection. It is well known that the Menger convexity is a generalization of the Takahashi convexity. In this article, we acquire a nonempty intersection property, in terms of the Hausdorff metric, for Menger convex metric spaces, that also provides a class of reflexive Menger convex spaces. We introduce a generalization of $(\alpha, \beta)-$generalized hybrid mapping, and using the obtained nonempty intersection property we derive the fixed point results for this generalized mapping defined on Menger convex spaces., Comment: 12 pages

The classical Cantor's intersection theorem states that in a complete metric space $X$, intersection of every decreasing sequence of nonempty closed bounded subsets, with diameter approaches zero, has exactly one point. In this article, we deal with decreasing sequences $\{K_n\}$ of nonempty closed bounded subsets of a metric space $X$, for which the Hausdorff distance $H(K_n, K_{n+1})$ tends to $0$, as well as for which the excess of $K_n$ over $X\setminus K_n$ tends to $0$. We achieve nonempty intersection properties in metric spaces. The obtained results also provide partial generalizations of Cantor's theorem., Comment: 9 pages

In distributed signal processing frames play significant role as redundant building blocks. Bemrose et. al. were motivated from this concept, as a result they introduced weaving frames in Hilbert space. Weaving frames have useful applications in sensor networks, likewise weaving K-frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator K. This article focuses on study, characterization of weaving K-frames in different spaces. Paley-Wiener type perturbation and conditions on erasure of frame components have been assembled to scrutinize woven-ness of K- frames., Comment: 9 pages

In a separable Hilbert space $\mathcal H$, two frames $\{f_i\}_{i \in I}$ and $\{g_i\}_{i \in I}$ are said to be woven if there are constants $0

K-fusion frames are generalizations of fusion frames in frame theory. This article characterizes various kinds of property of K-fusion frames. Several perturbation results on K-fusion frames are formulated and analyzed., Comment: 11 pages

This paper introduces the concept of atomic subspaces with respect to a bounded linear operator. Atomic subspaces generalize fusion frames and this generalization leads to the notion of $K$-fusion frames. Characterizations of $K$-fusion frames are discussed. Various properties of $K$-fusion frames, for example, direct sums, intersection, are studied., Comment: 11 pages, To appear in Indian Journal of Pure and Applied Mathematics (2020)

This paper proposes a new class of copulas which characterize the set of all twice continuously differentiable copulas. We show that our proposed new class of copulas is a new generalized copula family that include not only asymmetric copulas but also all smooth copula families available in the current literature. Spearman's rho and Kendall's tau for our new Fourier copulas which are asymmetric are introduced. Furthermore, an approximation method is discussed in order to optimize Spearman's rho and the corresponding Kendall's tau., Comment: 12 pages, 5 figures, Submitted