Outer Function Research Articles

Weighted Dirichlet spaces that are de Branges-Rovnyak spaces with equivalent norms

For a positive Borel measure μ in the unit disc, we examine which weighted Dirichlet spaces Dμ can be identified with de Branges-Rovnyak spaces Hb, with equivalent norms. We prove a necessary condition for the equality Dμ=Hb and we explore its consequences. For Carleson measures μ, we give a necessary and sufficient condition for the equality Dμ=Hbμ, for a certain outer function bμ related with the balayage of μ on the unit circle, and we provide examples of those spaces.

Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization

This paper presents a new approach that automates the tuning process in topology optimization of parameters that are traditionally defined by the user. The new method draws inspiration from hyperparameter optimization in machine learning. A new design problem is formulated where the topology optimization hyperparameters are defined as design variables and the problem is solved by surrogate optimization. The new design problem is nested, such that a topology optimization problem is solved as an inner problem. To encourage the identification of high-performing solutions while limiting the computational resource requirements, the outer objective function is defined as the original objective combined with penalization for intermediate densities and deviations from the prescribed material consumption. The contribution is demonstrated on density-based topology optimization with various hyperparameters and objectives, including compliance minimization, compliant mechanism design, and buckling load factor maximization. Consistent performance is observed across all tested examples. For a simple two hyperparameter case, the new framework is shown to reduce amount of times a topology optimization algorithm is executed by 90% without notably sacrificing the objective compared to a rigorous manual grid search.

Electroretinographic changes in the inner and outer retinal layers before and after intravenous chemotherapy for retinoblastoma.

To study the inner and outer retinal functions using a full-field electroretinogram (ERG) before and after intravenous chemotherapy (IVC) in children with retinoblastoma (RB). Of the 11 eyes, seven had RB and four were normal. All children were examined under anesthesia using a handheld ERG machine with a standard protocol - light-adapted single-flash ERG (fERG), photopic single-flash 3.0- and 30-Hz flickers, and photopic negative response (PhNR) amplitudes at 72 ms (P72). The amplitudes and peak times were compared before and after IVC. Post-chemotherapy tumor regressed in all seven eyes. Of the seven eyes, the fERG peak time (a-wave) was delayed in two eyes (29%), whereas the b-wave was delayed in six eyes (86%). The fERG amplitude height for a- and b-waves decreased in five eyes (71%) and six eyes (86%), respectively. In addition, photopic flicker 30-Hz b-wave peak time delayed in five eyes (71%), whereas the b-wave amplitude height decreased in six eyes (86%). Simultaneously, the P72 amplitude height decreased in six eyes (86%), whereas the P-ratio increased in all seven eyes (100%). In comparison, the ERG responses improved in three of the four contralateral normal eyes. Overall, the cone function improved in two eyes (29%), whereas cone bipolar cell and retinal ganglion cell (RGC) function improved in one eye (14%) each. Comparison of light-adapted ERG changes before and after IVC showed reduced amplitudes and delayed peak times for both a and b waveforms, as well as reduced PhNR amplitude attributable to bipolar and RGC injury.

Structure of the MlaC-MlaD complex reveals molecular basis of periplasmic phospholipid transport

The Maintenance of Lipid Asymmetry (Mla) pathway is a multicomponent system found in all gram-negative bacteria that contributes to virulence, vesicle blebbing and preservation of the outer membrane barrier function. It acts by removing ectopic lipids from the outer leaflet of the outer membrane and returning them to the inner membrane through three proteinaceous assemblies: the MlaA-OmpC complex, situated within the outer membrane; the periplasmic phospholipid shuttle protein, MlaC; and the inner membrane ABC transporter complex, MlaFEDB, proposed to be the founding member of a structurally distinct ABC superfamily. While the function of each component is well established, how phospholipids are exchanged between components remains unknown. This stands as a major roadblock in our understanding of the function of the pathway, and in particular, the role of ATPase activity of MlaFEDB is not clear. Here, we report the structure of E. coli MlaC in complex with the MlaD hexamer in two distinct stoichiometries. Utilising in vivo complementation assays, an in vitro fluorescence-based transport assay, and molecular dynamics simulations, we confirm key residues, identifying the MlaD β6-β7 loop as essential for MlaCD function. We also provide evidence that phospholipids pass between the C-terminal helices of the MlaD hexamer to reach the central pore, providing insight into the trajectory of GPL transfer between MlaC and MlaD.

Retinitis pigmentosa and stem cell therapy.

Retinitis pigmentosa (RP) is a group of genetic disorders characterized by progressive degeneration of photoreceptors and retinal pigment epithelium (RPE) cells. Its main clinical manifestations include night blindness and progressive loss of peripheral vision, making it a prevalent debilitating eye disease that significantly impacts patients' quality of life. RP exhibits significant phenotypic and genetic heterogeneity. For instance, numerous abnormal genes are implicated in RP, resulting in varying clinical presentations, disease progression rates, and pathological characteristics among different patients. Consequently, gene therapy for RP poses challenges due to these complexities. However, stem cells have garnered considerable attention in the field of RPE therapy since both RPE cells and photoreceptors can be derived from stem cells. In recent years, a large number of animal experiments and clinical trials based on stem cell transplantation attempts, especially cord blood mesenchymal stem cell (MSC) transplantation and bone marrow-derived MSC transplantation, have confirmed that stem cell therapy can effectively and safely improve the outer retinal function of the RP-affected eye. However, stem cell therapy also has certain limitations, such as the fact that RP patients may involve multiple types of retinal cytopathia, which brings great challenges to stem cell transplantation therapy, and further research is needed to solve various problems faced by this approach in the clinic. Through comprehensive analysis of the etiology and histopathological changes associated with RP, this study substantiates the efficacy and safety of stem cell therapy based on rigorous animal experimentation and clinical trials, while also highlighting the existing limitations that warrant further investigation.

Local convergence of augmented Lagrangian methods for composite optimization

In this paper, we propose an augmented Lagrangian method for composite optimization with the outer function satisfying the second order epi-regular property. The local convergence and rate of convergence of this algorithm will be proved under the assumptions of the second order sufficient condition via the second order epi-derivative of augmented Lagrangian and the semi-isolated calmness of the solution mapping of perturbed generalized equation formulated from KKT system. For the penalty parameters large enough, we obtain the primal-dual Q-linear convergence rate.

Continuity of inner-outer factorization and cross sections from invariant subspaces to inner functions

Let H∞ be the Banach algebra of bounded analytic functions on the unit open disc D equipped with the supremum norm. As well known, inner functions play an important role in the study of bounded analytic functions. In this paper, we are interested in the study of inner functions. Following by the canonical inner-outer factorization decomposition, define Qinn and Qout the maps from H∞ to I the set of inner functions and F the set of outer functions, respectively. In this paper, we study the H2-norm continuity and H∞-norm discontinuity of Qinn and Qout on some subsets of H∞. On the other hand, the Beurling theorem connects inner functions and invariant subspaces of the multiplication operator Mz. We show the nonexistence of continuous cross section from some certain invariant subspaces to inner functions in the supremum norm. The continuity problem of Qinn and Qout on Hol(D‾), the set of all analytic functions in the closed unit disk, are considered. In addition, we also study the factor maps Q[inn] and Q[out] from H∞ to I/T and F/T, where I/T is the quotient space of I mod T and F/T is the quotient space of F mod T.

On application of Gaussian kernels and Laplace functions combined with Kolmogorov's theorem for approximation of functions of several variables

A special class of approximations of measurable functions of several variables on the unit coordinate cube is investigated. The class is constructed on the base of Kolmogorov's theorem (in version by Sprecher–Golubkov) stating that a continuous function $f$ of several variables can be represented as a finite superposition of continuous single-variable functions — so called outer functions (which depend of $f$) and inner one $\Psi$ (which is independent of $f$ and is monotone). In the case of continuous functions $f$ the class under study is obtained with outer functions approximated by linear combinations of quadratic exponentials (also known as Gaussian functions or Gaussian kernels) and with the inner function $\Psi$ approximated by Laplace functions. As is known, a measurable function $f$ can be approximated by a continuous one (up to a set of small measure) with the help of classical Luzin's theorem. The effectiveness of such approach is based on assertions that, firstly, the Mexican hat mother wavelet on any fixed bounded interval can be approximated as accurately as desired by a linear combination of two Gaussian functions, and, secondly, that a continuous monotone function on such an interval can be approximated as accurately as desired by a linear combination of translations and dilations of the Laplace integral (in other words, Laplace functions). It is proved that the class of approximations under study is dense everywhere in the class of continuous multivariable functions on the coordinate cube. For the case of continuous and piecewise continuous functions of two variables, numerical results are presented that confirm the effectiveness of approximations of the studied class.

Porous and Meltable Metal-Organic Polyhedra for the Generation and Shaping of Porous Mixed-Matrix Composites.

Here, we report the synthesis of BCN-93, a meltable, functionalized, and permanently porous metal-organic polyhedron (MOP) and its subsequent transformation into amorphous or crystalline, shaped, self-standing, transparent porous films via melting and subsequent cooling. The synthesis entails the outer functionalization of a MOP with meltable polymer chains: in our model case, we functionalized a Rh(II)-based cuboctahedral MOP with poly(ethylene glycol). Finally, we demonstrate that once melted, BCN-93 can serve as a porous matrix into which other materials or molecules can be dispersed to form mixed-matrix composites. To illustrate this, we combined BCN-93 with one of various additives (either two MOF crystals, a porous cage, or a linear polymer) to generate a series of mixed-matrix films, each of which exhibited greater CO2 uptake relative to the parent film.

ITF2357 regulates NF-κB signaling pathway to protect barrier integrity in retinal pigment epithelial cells.

The robust integrity of the retinal pigment epithelium (RPE), which contributes to the outer brain retina barrier (oBRB), is compromised in several retinal degenerative and vascular disorders, including diabetic macular edema (DME). This study evaluates the role of a new generation of histone deacetylase inhibitor (HDACi), ITF2357, in regulating outer blood-retinal barrier function and investigates the underlying mechanism of action in inhibiting TNFα-induced damage to RPE integrity. Using the immortalized RPE cell line (ARPE-19), ITF2357 was found to be non-toxic between 50 nM and 5 μM concentrations. When applied as a pre-treatment in conjunction with an inflammatory cytokine, TNFα, the HDACi was safe and effective in preventing epithelial permeability by fortifying tight junction (ZO-1, -2, -3, occludin, claudin-1, -2, -3, -5, -19) and adherens junction (E-cadherin, Nectin-1) protein expression post-TNFα stress. Mechanistically, ITF2357 depicted a late action at 24 h via attenuating IKK, IκBα, and p65 phosphorylation and ameliorated the expression of IL-1β, IL-6, and MCP-1. Also, ITF2357 delayed IκBα synthesis and turnover. The use of Bay 11-7082 and MG132 further uncovered a possible role for ITF2357 in non-canonical NF-κB activation. Overall, this study revealed the protection effects of ITF2357 by regulating the turnover of tight and adherens junction proteins and modulating NF-κB signaling pathway in the presence of an inflammatory stressor, making it a potential therapeutic application for retinal vascular diseases such as DME with compromised outer blood-retinal barrier.

Photoionization of Nitrile-substituted Naphthalene and Benzene: Cation Spectroscopy, Photostability, and Implications for Photoelectric Gas Heating

We investigate the vacuum ultraviolet (VUV) photodynamics of gas phase 1- and 2-cyanonaphthalene and cyanobenzene, recently detected in the Taurus molecular cloud, by combining synchrotron radiation and a double imaging electron/ion coincidence setup. The high-resolution threshold photoelectron spectra (TPES) of all three molecules are obtained experimentally from which the adiabatic ionization energies are reported with very high accuracy, particularly for 2-cyanonaphthalene, for which no data exist at this level of precision. Theoretical calculations are performed to compare with the TPES for the ground electronic state of the cations. Furthermore, the different features observed in the extended TPES have been assigned to the different molecular orbitals with the help of the outer valence Green's function calculations. The present experiments also shed light on the kinetic energy distribution of the photoelectrons as a function of the incident photon energy, to describe their contribution to the photoelectric heating effect in the interstellar medium. In this context, we show how kinetic energy distributions can be obtained from our data for any given photon energy, such as the omnipresent Lyα line, or any given interstellar radiation field (ISRF). In addition, from the total ion yields, we estimate the photorates for a few ISRFs. Finally, we discuss the photodissociation of the two cyanonaphthalenes, quoting the activation energies of the dissociation channels with the help of Rice–Ramsperger–Kassel–Marcus modeling. It is observed that CN substitution does not cause any appreciable change to the VUV dissociative photoionization relaxation channel.

The Mla system and its role in maintaining outer membrane barrier function in Stenotrophomonas maltophilia.

Stenotrophomonas maltophilia are ubiquitous Gram-negative bacteria found in both natural and clinical environments. It is a remarkably adaptable species capable of thriving in various environments, thanks to the plasticity of its genome and a diverse array of genes that encode a wide range of functions. Among these functions, one notable trait is its remarkable ability to resist various antimicrobial agents, primarily through mechanisms that regulate the diffusion across cell membranes. We have investigated the Mla ABC transport system of S. maltophilia, which in other Gram-negative bacteria is known to transport phospholipids across the periplasm and is involved in maintaining outer membrane homeostasis. First, we structurally and functionally characterized the periplasmic substrate-binding protein MlaC, which determines the specificity of this system. The predicted structure of the S. maltophilia MlaC protein revealed a hydrophobic cavity of sufficient size to accommodate the phospholipids commonly found in this species. Moreover, recombinant MlaC produced heterologously demonstrated the ability to bind phospholipids. Gene knockout experiments in S. maltophilia K279a revealed that the Mla system is involved in baseline resistance to antimicrobial and antibiofilm agents, especially those with divalent-cation chelating activity. Co-culture experiments with Pseudomonas aeruginosa also showed a significant contribution of this system to the cooperation between both species in the formation of polymicrobial biofilms. As suggested for other Gram-negative pathogenic microorganisms, this system emerges as an appealing target for potential combined antimicrobial therapies.

Parameteric optimization of SiGe S/D NT JLFET using analytical modeling to improve L‐BTBT induced GIDL

AbstractIn the present work, we investigate the impact of structure dimensional parameters on the short channel effects which occurs especially below 20 nm regime particularly gate induced drain leakage (GIDL) current. Using technology computer aided design simulation (TCAD), we have examined the GIDL for SiGe as source/drain in NTJLFET. The structural dimensional parameters such as the nanotube thickness, core and outer gates thickness and gate electrode work function shows the significant impact on the band to band tunneling in lateral direction (L‐BTBT) which induced GIDL current. It is analyzed that increase in the nanotube thickness and physical oxide thickness increase the GIDL current, while increasing the gate electrode work function, core gate and outer gate thicknesses gives reduced GIDL current. The SiGe S/D NTJLFET produce a remarkable high ION/IOFF ratio ~ 1011. A compact model for GIDL current is also developed which shows the dependency of structure parameters on leakage current. The SiGe has been incorporated as source and drain in NTJLFET which creates the energy band discontinuity. Furthermore, SiGe S/D NTJLFET is fairly compared with the conventional NT JLFET and nanowire (NW) JLFET and shows an improved performance.

CP-AFM Molecular Tunnel Junctions with Alkyl Backbones Anchored Using Alkynyl and Thiol Groups: Microscopically Different Despite Phenomenological Similarity.

In this paper, we report results on the electronic structure and transport properties of molecular junctions fabricated via conducting probe atomic force microscopy (CP-AFM) using self-assembled monolayers (SAMs) of n-alkyl chains anchored with acetylene groups (CnA; n = 8, 9, 10, and 12) on Ag, Au, and Pt electrodes. We found that the current-voltage (I-V) characteristics of CnA CP-AFM junctions can be very accurately reproduced by the same off-resonant single-level model (orSLM) successfully utilized previously for many other junctions. We demonstrate that important insight into the energy-level alignment can be gained from experimental data of transport (processed via the orSLM) and ultraviolet photoelectron spectroscopy combined with ab initio quantum chemical information based on the many-body outer valence Green's function method. Measured conductance GAg < GAu < GPt is found to follow the same ordering as the metal work function ΦAu < ΦAu < ΦPt, a fact that points toward a transport mediated by an occupied molecular orbital (MO). Still, careful data analysis surprisingly revealed that transport is not dominated by the ubiquitous HOMO but rather by the HOMO-1. This is an important difference from other molecular tunnel junctions with p-type HOMO-mediated conduction investigated in the past, including the alkyl thiols (CnT) to which we refer in view of some similarities. Furthermore, unlike in CnT and other junctions anchored with thiol groups investigated in the past, the AFM tip causes in CnA an additional MO shift, whose independence of size (n) rules out significant image charge effects. Along with the prevalence of the HOMO-1 over the HOMO, the impact of the "second" (tip) electrode on the energy level alignment is another important finding that makes the CnA and CnT junctions different. What ultimately makes CnA unique at the microscopic level is a salient difference never reported previously, namely, that CnA's alkyne functional group gives rise to two energetically close (HOMO and HOMO-1) orbitals. This distinguishes the present CnA from the CnT, whose HOMO stemming from its thiol group is well separated energetically from the other MOs.

Altered Outer Retinal Structure, Electrophysiology and Visual Perception in Parkinson's Disease.

Visual biomarkers of Parkinson's disease (PD) are attractive as the retina is an outpouching of the brain. Although inner retinal neurodegeneration in PD is well-established this has overlap with other neurodegenerative diseases and thus outer retinal (photoreceptor) measures warrant further investigation. To examine in a cross-sectional study whether clinically implementable measures targeting outer retinal function and structure can differentiate PD from healthy ageing and whether these are sensitive to intraday levodopa (L-DOPA) dosing. Centre-surround perceptual contrast suppression, macular visual field sensitivity, colour discrimination, light-adapted electroretinography and optical coherence tomography (OCT) were tested in PD participants (n = 16) and controls (n = 21). Electroretinography and OCT were conducted before and after midday L-DOPA in PD participants, or repeated after ∼2 hours in controls. PD participants had decreased center-surround contrast suppression (p < 0.01), reduced macular visual field sensitivity (p < 0.05), color vision impairment (p < 0.01) photoreceptor dysfunction (a-wave, p < 0.01) and photoreceptor neurodegeneration (outer nuclear layer thinning, p < 0.05), relative to controls. Effect size comparison between inner and outer retinal parameters showed that photoreceptor metrics were similarly robust in differentiating the PD group from age-matched controls as inner retinal changes. Electroretinography and OCT were unaffected by L-DOPA treatment or time. We show that outer retinal outcomes of photoreceptoral dysfunction (decreased cone function and impaired color vision) and degeneration (i.e., outer nuclear layer thinning) were equivalent to inner retinal metrics at differentiating PD from healthy age-matched adults. These findings suggest outer retinal metrics may serve as useful biomarkers for PD.

A method for solving the limit of multivariate composite functions

Abstract In this paper, according to the concept of multivariate composite function, the limit and continuity conditions of multivariate composite function are given, and the continuity relationship between the inner function and the outer function of the composite function at the same point is investigated. The relationship between the limit and continuity of a composite function composed of two functions at the same point is investigated by examples, while some limit results are explained from the perspective of composite functions, and the limit calculation law of multivariate composite functions is proposed. Using the consistent central limit theorem in the limit calculation law, the absolute value and limit of the interval of the multivariate composite function are obtained, and the iterative limit of the variational reduction approximation method is confirmed by combining the absolute value and limit of the interval of the multivariate composite function. On the basis of the application of limit operation of a multivariate composite function, the limit distribution of high-dimensional likelihood ratio statistics of multivariate composite function is analyzed by using data simulation analysis. The results show that both limit distributions have better simulation results when p are small, such as p = 5 or p = 10, but the traditional limit is better than the normal limit, indicating that the results of multivariate composite function limit calculations have good accuracy. A method for solving the limits of multivariate composite functions is proposed in this study, which is of great theoretical and practical significance in the study of higher mathematics.

Contributed Session I: Correlating cone structure and function in retinitis pigmentosa using coarse-scale optoretinography (CoORG).

Optoretinography (ORG) has the potential to serve as a powerful diagnostic biomarker, owing to its sensitive and objective localization of function and dysfunction. Majority of ORG implementations employ adaptive optics (AO) for imaging activity at a cellular scale. Coarse-scale Optoretinography (CoORG), an ORG paradigm without AO, offers rapid, extended-field recordings and wider applicability in patients with retinal disease, by compromising cellular resolution. This study investigates the feasibility of CoORG in assessing cone dysfunction in patients diagnosed with retinitis pigmentosa (RP). Five RP patients aged 26 - 60 were recruited, alongside age-similar controls. The stimulus for evoking cone activity had a photon density between 15.5x10e6 - 19.7x10e6 photons/μm2, and was centered at 532 ± 5nm. Eight imaging trials per bleach were performed, allowing for 1 min. between successive trials for dark adaptation. The total experimental time for each bleach was 10-20 mins. In RP, cone function, estimated as the change in optical path length in the outer segment in response to a stimulus, was diminished and generally lower than normal controls. This deficit was observed in areas of seemingly normal outer retinal structure. Contrary to normals, no correlation was observed between outer segment length and cone function in RP. This highlights CoORG's potential for early, sensitive detection of retinal dysfunction prior to apparent structural degradation.

Approximation of curve-based sleeve functions in high dimensions

Sleeve functions are generalizations of the well-established ridge functions that play a major role in the theory of partial differential equation, medical imaging, statistics, and neural networks. Where ridge functions are non-linear, univariate functions of the distance to hyperplanes, sleeve functions are based on the squared distance to lower-dimensional manifolds. The present work is a first step to study general sleeve functions by starting with sleeve functions based on finite-length curves. To capture these curve-based sleeve functions, we propose and study a two-step method, where first the outer univariate function—the profile—is recovered, and second, the underlying curve is represented by a polygonal chain. Introducing a concept of well-separation, we ensure that the proposed method always terminates and approximates the true sleeve function with a certain quality. Investigating the local geometry, we study an inexact version of our method and show its success under certain conditions.

Effects of uranium mining on soil bacterial communities and functions in the Qinghai-Tibet plateau

The microecological effects of plateau uranium mining are still unknown. In this study, we used 16S rRNA high-throughput sequencing to analyze the impact of plateau uranium mining on the microbial diversity and community structure of tailings soil, tunnel soil, and soil at different depths in an open pit. The results showed that uranium mining significantly reduced soil microbial community richness and diversity indicators, including Chao1, Pielou evenness, and Shannon index (P < 0.05). Uranium mining activities significantly reduced the abundance of RB41, Vicinamidactaceae, and Nitrospira (P < 0.05). Interestingly, the abundance of Thiobacillus, Sphingomonas, and Sulfuriferula significantly increased in the soil samples from various environments and depths during uranium mining (P < 0.05). Beta diversity analysis found that uranium mining resulted in the differentiation of soil microbial communities. Functional enrichment analysis found that uranium mining resulted in the functional enrichment of DNA binding response regulator, DNA helicase, methyl-accepting chemotaxis protein, and Helicase conserved C-terminal domain, whereas cell wall synthesis, nonspecific serine/threonine protein kinase, RNA polymerase sigma-70 factor, and ATP binding cassette transporter were significantly affected by uranium mining (P < 0.05). In addition, we also found that different uranium mining environments and soil depths enriched diverse microbial populations and functions to cope with the environmental pressures that were elicited by uranium mining, including Gaiella, Gemmatimonas, Lysobacter, Pseudomonas, signal transformation histidine kinase, DNA-directed DNA polymerase, and iron complex outer membrane receptor protein functions (P < 0.05). The results have enhanced our understanding of the impact of uranium mining on plateau soil microecological stability and the mechanism of microbial response to uranium mining activities for the first time and aided us in screening microbial strains that can promote the environmental remediation of uranium mining in plateaus.

A note on Bohr’s theorem for Beurling integer systems

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