Vector Topology Research Articles

The impact of expression vector position on transgene transcription allows for rational expression vector design in a targeted integration system.

Site-specific integration (SSI) technology has emerged as an effective approach by the pharmaceutical industry for the development of recombinant Chinese hamster ovary (CHO) cell lines. While SSI systems have been demonstrated to be effective for the development of CHO cell lines, they can be limiting in terms of both transgene expression and in the case of multi-specifics, the ability to generate the correct product of interest. To maximize the performance of Pfizer's dual SSI expression system for expressing monoclonal and multi-specific antibodies, we used a novel approach to investigate the positional effect of transgenes within expression vectors by engineering nucleotide polymorphisms (NP)s to use as biomarkers to track the level of transcript output from each expression vector position. We observed differences in transcript level for two different transgenes across all four expression vector positions interrogated. We then applied these learnings to rationally design expression vectors for six different mAbs and a multi-specific antibody. We showed enhanced productivity and optimal product quality when compared to a conventional expression vector topology. The learnings gained here can potentially aid in the determination of optimal vector topologies for several IgG-like multi-specific formats.

Compatible topologies on mixed lattice vector spaces

A mixed lattice vector space is a partially ordered vector space with two partial orderings, generalizing the notion of a Riesz space. The purpose of this paper is to develop the basic topological theory of mixed lattice spaces. A vector topology is said to be compatible with the mixed lattice structure if the mixed lattice operations are continuous. We give a characterization of compatible mixed lattice topologies, similar to the well known Roberts-Namioka characterization of locally solid Riesz spaces. We then study locally convex topologies and the associated seminorms, as well as connections between mixed lattice topologies and locally solid topologies on Riesz spaces. In the locally convex case, we obtain a more complete characterization of compatible mixed lattice topologies. We also briefly discuss asymmetric norms and cone norms on mixed lattice spaces with a particular application to finite dimensional spaces.

Engineering circular RNA for enhanced protein production

Circular RNAs (circRNAs) are stable and prevalent RNAs in eukaryotic cells that arise from back-splicing. Synthetic circRNAs and some endogenous circRNAs can encode proteins, raising the promise of circRNA as a platform for gene expression. In this study, we developed a systematic approach for rapid assembly and testing of features that affect protein production from synthetic circRNAs. To maximize circRNA translation, we optimized five elements: vector topology, 5′ and 3′ untranslated regions, internal ribosome entry sites and synthetic aptamers recruiting translation initiation machinery. Together, these design principles improve circRNA protein yields by several hundred-fold, provide increased translation over messenger RNA in vitro, provide more durable translation in vivo and are generalizable across multiple transgenes.

Positive filters and links in an ℓ-group

In this paper we continue our research about links and link topologies on ℓ-groups and Riesz spaces. We show that in a Riesz space E, a link topology τ is a vector topology, if and only if the link consists of all order units in E. We also compare the link topologies with the positive filter topologies on an ℓ-group. In addition, we provide some examples of these constructions.

Non-Linear Inner Structure of Topological Vector Spaces

Inner structure appeared in the literature of topological vector spaces as a tool to characterize the extremal structure of convex sets. For instance, in recent years, inner structure has been used to provide a solution to The Faceless Problem and to characterize the finest locally convex vector topology on a real vector space. This manuscript goes one step further by settling the bases for studying the inner structure of non-convex sets. In first place, we observe that the well behaviour of the extremal structure of convex sets with respect to the inner structure does not transport to non-convex sets in the following sense: it has been already proved that if a face of a convex set intersects the inner points, then the face is the whole convex set; however, in the non-convex setting, we find an example of a non-convex set with a proper extremal subset that intersects the inner points. On the opposite, we prove that if a extremal subset of a non-necessarily convex set intersects the affine internal points, then the extremal subset coincides with the whole set. On the other hand, it was proved in the inner structure literature that isomorphisms of vector spaces and translations preserve the sets of inner points and outer points. In this manuscript, we show that in general, affine maps and convex maps do not preserve inner points. Finally, by making use of the inner structure, we find a simple proof of the fact that a convex and absorbing set is a neighborhood of 0 in the finest locally convex vector topology. In fact, we show that in a convex set with internal points, the subset of its inner points coincides with the subset of its internal points, which also coincides with its interior with respect to the finest locally convex vector topology.

MMIC Vector Topology Enabling Multi RF Functionalities for 5G and Beyond

This paper presents a vector topology of a monolithic microwave integrated circuit (MMIC) capable of performing several radiofrequency (RF) functionalities essential for future wireless communications and geolocation in the millimeter frequency band. The proposed circuit can address several usage modes such as conventional frequency heterodyning for high-speed IQ modulation and demodulation. In addition, the device can be configured in six-port quadratic detection mode to achieve optimum power added efficiency (PAE). The topology developed in 65 nm FDSOI CMOS technology achieves broadband V-band frequency operation and combines vector precision for both high data rates and phase state determination. The results presented concern QPSK modulation schemes at data rates up to 4 Gbps as well as essential geolocation metrics such as time domain of arrival (TDoA) and angle of arrival (AoA). The combination of vector accuracy/PAE together with wide linear operating range makes this topology a viable candidate for next generation radio frequency systems.

Mackey continuity of convex functions on dual Banach spaces: a review

A convex (or concave) real-valued function, f , on a dual Banach space P is continuous for the Mackey topology m (P∗, P ) if (and only if) it is Mackey continuous on bounded subsets of P∗ . Equivalence of Mackey continuity to sequential Mackey continuity follows when P is strongly weakly compactly generated, e.g., when P = L1(T ), where T is a set that carries a sigma-finite measure σ. This result of Delbaen, Orihuela and Owari extends their earlier work on the case that P∗ is either L∞ (T ) or a dual Orlicz space. An earlier result of this kind is recalled also: it derives Mackey continuity from bounded Mackey continuity for a nondecreasing concave function, F , that is defined and finite only on the nonnegative cone L∞+. Applied to a linear f , the Delbaen-Orihuela-Owari result shows that the convex bounded Mackey topology is identical to the Mackey topology, i.e., cbm (P∗, P ) = m (P∗, P ); here, this is shown to follow also from Grothendieck’s Completeness Theorem. As for the bounded Mackey topology, bm (P∗, P ), it is conjectured here not to be a vector topology, or equivalently to be strictly stronger than m (P∗, P ), except when P is reflexive.

Fuzzy Granule Manifold Alignment Preserving Local Topology

Granular computing has the advantage of discovering complex data knowledge, and manifold alignment has proven of great value in a lot of areas of machine learning. We propose a novel algorithm of fuzzy granule manifold alignment (FGMA), where we define some new operations, measurements, and local topology of fuzzy granular vectors in fuzzy granular space. Furthermore, the algorithm is very different from Semi-supervised and Procrustes algorithm because predetermining correspondence is not necessary. A projection is learned that can map instances described by two types of features to a low-dimensional space. Meanwhile, the local topology of the fuzzy granular vector induced by the instance is also preserved and matched within each set in lower dimensional space. This approach makes it possible to directly compare between data instances in different spaces. We convert an alignment problem of data in feature space into fuzzy granular manifold alignment problem of granular space. Specifically, we first define fuzzy granule, fuzzy granular vector, operations, and measurements in fuzzy granular space and gave proofs of theorems and deductions. Next, the local topology around the fuzzy granular vector is introduced and the optimal local topology matching can be achieved by minimizing their Frobenius norm. Finally, two manifolds are connected and the optimal mapping can be calculated to obtain dimensionality reduction of the joint structure. Thus, the corresponding relationship between two data instances can be got. We verified this algorithm in Oxford image and Alzheimer’s disease voice dataset. Theoretical analysis and experiments demonstrate the algorithm proposed is robust and effective.

A Solution to the Faceless Problem

Internal points were introduced in the literature of topological vector spaces to characterize the finest locally convex vector topology. Later on, they have been generalized to the context of real vector spaces by means of the inner points. Inner points can be seen as the most opposite concept to the extreme points. In this manuscript we solve the “faceless problem”, that is, the informally posed open problem of characterizing those convex sets free of proper faces. Indeed, we prove that a non-singleton convex subset of a real vector space is free of proper faces if and only if every point of the convex set is an inner point. As a consequence, we prove the following dichotomy theorem: a point of a convex set of a real vector space is either a extreme point or an inner point of some face. We also characterize the non-singleton closed convex subsets of a topological vector space free of proper faces, which turn out to be the linear manifolds. An application of this allows us to show that the only possible minimal faces of a linearly bounded closed convex subset of a topological vector space are the extreme points. As an application of the technique we develop to prove our results, we easily construct dense proper faces of convex sets and non-dense proper faces whose closure is not a face. This fact allows us to equivalently renorm any infinite dimensional Banach space so that its unit ball contains a non-closed face. Even more, we prove that every infinite dimensional Banach space containing an isomorphic copy of $$c_0$$ or $$\ell _p$$ , $$1<p<\infty $$ , can be equivalently renormed so that its unit ball contains a face whose closure is not a face.

On the topological structure of a Hahn field and convergence of power series

In this paper, we study the topological structure of the Hahn field F whose elements are functions from the additive abelian group of rational numbers Q to the real numbers field R, with well-ordered support. After reviewing the algebraic and order structures of the field F, we introduce different vector topologies on F that are induced by families of semi-norms, all of which are weaker than the order or valuation topology. We compare those vector topologies and we identify the weakest one which we denote by τw and whose properties are similar to those of the weak topology on the Levi-Civita field (Shamseddine, 2010). In particular, we state and prove a convergence criterion for power series in F,τw that is similar to that for power series on the Levi-Civita field in its weak topology (Shamseddine, 2013).

Relative interior and closure of the set of inner points

Internal points were introduced in the literature of topological vector spaces to characterize the finest locally convex vector topology. Very recently this concept was generalized to the one of inner points in the scope of vector spaces, which, among other things, allows to characterize the linear dimension of a vector space and also serves to provide an intrinsic characterization of linear manifolds that was not possible by using internal points. Inner points of convex sets can be seen as the affine internal points, that is, the internal points with respect to the affine hull. In this manuscript we continue this research line in the scope of topological vector spaces to study the topological structure of the inner points. First, we prove that every infinite dimensional vector space has a convex subset free of inner points which is dense in every vector topology the vector space is endowed with. Also, we find the existence of convex sets in which the set of inner points is not open in the relative topology. Following this line, we also characterize the closed convex sets for which the set of inner points is not empty and open in the relative topology. Finally, we find an example of a convex set whose set of inner points is not contained in the set of inner points of its closure.

Inner structure in real vector spaces

Abstract Internal points were introduced in the literature of topological vector spaces to characterize the finest locally convex vector topology. In this manuscript we generalize the concept of internal point in real vector spaces by introducing a type of points, called inner points, that allows us to provide an intrinsic characterization of linear manifolds, which was not possible by using internal points. We also characterize infinite dimensional real vector spaces by means of the inner points of convex sets. Finally, we prove that in convex sets containing internal points, the set of inner points coincides with the one of internal points.

Free multi-floor indoor space extraction from complex 3D building models

Intelligent navigation and facility management in complex indoor environments are issues at the forefront of geospatial information science. Indoor spaces with fine geometric and semantic descriptions provide a solid foundation for various indoor applications, but it is difficult to comprehensively extract free multi-floor indoor spaces from complex three-dimensional building models, such as those described using CityGML LoD4, with existing methods for the subdivision or extraction of indoor spaces based on vector topology processing. Therefore, this paper elaborates a new voxelbased approach for extracting free multi-floor indoor spaces from 3D building models. It transforms the complicated vector processing tasks into a simple raster process that consists of three steps: voxelization with semantic enhancement, voxel classification, and boundary extraction. Experiments illustrate that the proposed method can automatically and correctly extract free multi-floor indoor spaces, especially two typical kinds of open indoor spaces, namely, lobbies and staircases.

Bounded and Semi Bounded Inverse Theorems in Fuzzy Normed Spaces

In this paper, the author introduces the notion of the complete fuzzy norm on a linear space. And the author considers some relations between the fuzzy completeness and ordinary completeness on a linear space, moreover a new form of fuzzy compact spaces, namely b-compact spaces, b-closed space is introduced. Some characterization of their properties is obtained. Also some basic properties for linear operators between fuzzy normed spaces are further studied. The notions of fuzzy vector spaces and fuzzy topological vector spaces were introduced in Katsaras and Liu (1977). These ideas were modified by Katsaras (1981), and in (1984) Katsaras defined the fuzzy norm on a vector space. In (1991) Krishna and Sarma discussed the generation of a fuzzy vector topology from an ordinary vector topology on vector spaces. Also Krishna and Sarma (1992) observed the convergence of sequence of fuzzy points. Rhie et al. (1997) Introduced the notion of fuzzy a-Cauchy sequence of fuzzy points and fuzzy completeness.

Optimized Space Vector Pulse-width Modulation Technique for a Five-level Cascaded H-Bridge Inverter

This paper presents an optimized space vector pulse-width modulation (OSVPWM) technique for a five-level cascaded H-bridge (CHB) inverter. The space vector diagram of the five-level CHB inverter is optimized by resolving it into inner and outer two-level space vector hexagons. Unlike conventional space vector topology, the proposed technique significantly reduces the involved computational time and efforts without compromising the performance of the five-level CHB inverter. A further optimized (FOSVPWM) technique is also presented in this paper, which significantly reduces the complexity and computational efforts. The developed techniques are verified through MATLAB/SIMULINK. Results are compared with sinusoidal pulse-width modulation (SPWM) to prove the validity of the proposed technique. The proposed simulation system is realized by using an XC3S400 field-programmable gate array from Xilinx, Inc. The experiment results are then presented for verification.

Impact of DNA vector topology on non-viral gene therapeutic safety and efficacy.

Gene therapy continues to grow as an emerging treatment strategy toward numerous diseases. However, such prospects are hindered by the use of viral vectors prompting significant safety concerns along with limitations concerning repeat administrations, size of delivered gene construct, scale-up, high production costs, contamination during production, and lack of desired tissue selectivity. Non-viral gene delivery demonstrates the potential to address the abovementioned limitations, but itself generally suffers from low efficacy. Continuing efforts have been made to develop innovative delivery systems, synthetic gene carriers, and DNA vectors in a concerted attempt to enhance gene delivery suitable for clinical applications. In this review, we focus on the advances in the design of novel DNA vectors catered to enhance transfection and transgene expression and their influences on the efficacy and safety of existing and emerging delivery systems and synthetic vectors for non viral gene delivery.

Modified self-organising maps with a new topology and initialisation algorithm

Mapping quality of the self-organising maps (SOMs) is sensitive to the map topology and initialisation of neurons. In this article, in order to improve the convergence of the SOM, an algorithm based on split and merge of clusters to initialise neurons is introduced. The initialisation algorithm speeds up the learning process in large high-dimensional data sets. We also develop a topology based on this initialisation to optimise the vector quantisation error and topology preservation of the SOMs. Such an approach allows to find more accurate data visualisation and consequently clustering problem. The numerical results on eight small-to-large real-world data sets are reported to demonstrate the performance of the proposed algorithm in the sense of vector quantisation, topology preservation and CPU time requirement.

On some relationships between biorthogonal systems, linear topologies and the weak‐AFPP

In this paper, we obtain new results for the weak‐AFPP in abstract spaces by exploiting biorthogonal systems techniques. Firstly, we investigate the strong‐AFPP on countably infinite dimensional Hausdorff locally convex spaces. Spaces of this class are shown to be sequentially complete iff they have the hereditary FPP for totally bounded, closed convex sets. This might open a research line for the analysis of weak‐AFPP in such frames. In connection, we provide a simple criterion for the containement of ℓ1‐sequences in terms of strongly‐equicontinuous biorthogonal systems. We then establish a few results concerning the existence of Hausdorff finer vector topologies on abstract spaces having as prescribed condition the existence of such systems. The proofs are based on methods of Peck and Porta concerning building of finer vector topologies, and a classical construction of Singer which allows us to prove under rather natural conditions the existence of equicontinuous biorthogonal systems in metrizable locally convex spaces. These results are compatible with the failure of the weak‐AFPP. We also study the inverse problem by proving that every infinite dimensional vector space admits a (non‐locally convex) Hausdorff vector topology which is complete, non‐metrizable and is compatible with a bounded Hamel Schauder basis. It is shown further that such a topology has the ‐AFPP, where is the linear span of coefficient functionals associated to a Hamel basis. Finally, inspired by a result of Shapiro, we observe that if X is a non‐locally convex F‐space with an absolute basis, then the weak‐AFPP is equivalent to the fact that every bounded convex subset of X is compact.

Maximal vector topologies

Suppose that κ is an infinite cardinal, Vκ=⊕α<κRα is a vector space of dimension κ over R, τκ is the box topology on Vκ, μκ and νκ are the maximal and maximal locally convex vector topologies on Vκ respectively. We prove that τω=μω=νω but, for every κ>ω, μκ⊃νκ⊃τκ. For every κ, the topological vector spaces (Vκ,μκ), (Vκ,νκ), (Vκ,τκ) are complete but not sequential.

Role of DNA topology in uptake of polyplex molecules by dendritic cells.

Dendritic cells (DCs) are an attractive target for DNA vaccines as they are potent antigen presenting cells. This study demonstrated how non-viral gene delivery to DCs involving complexes of poly-l-lysine (PLL) and plasmid DNA (pDNA) (polyplexes) showed dependence on DNA vector topology. DNA topology is of importance from both production and regulatory viewpoints. In our previous study with CHO cells we demonstrated that polyplex uptake was dependent on DNA topology whereby complexes containing supercoiled (SC) pDNA were smaller, more resistant to nucleases and more effectively condensed by PLL than open circular (OC) and linear-pDNA complexes. In this study polyplex uptake in DCs was measured qualitatively and quantitatively by confocal microscopy along with gene expression studies and measurement of DC phenotype. PLL is known for its ability to condense DNA and serve as an effective gene delivery vehicle. Quantification studies revealed that by 1h following uptake 15% (±2.59% relative standard error [RSE]) of SC-pDNA polyplexes were identified to be associated (fluorescent co-localisation) with the nucleus, in comparison to no nuclear association identified for OC- and linear-pDNA complexes. By 48 h following uptake, 30% (±1.82% RSE) of SC-pDNA complexes associated with the nucleus in comparison to 16% (±4.40% RSE) and 12% (±6.97% RSE) of OC- and linear-pDNA polyplexes respectively. Confocal microscopy images showed how DNA and PLL remained associated following uptake by dual labelling. Polyplex (containing 20 μg pDNA) gene expression (plasmid encoded lacZ [β-galactosidase] reporter gene) in DCs was greatest for SC-pDNA polyplexes at 14.12% unlike that of OC- (9.59%) and linear-pDNA (7.43%). DCs express cell surface markers which contribute towards antigen presentation. Polyplex gene expression did not alter DC phenotype through surface marker expression. This may be due to the pDNA dose employed (20μg) as other studies have used doses as high as 200 μg pDNA to induce DC phenotypic changes. Although no change in DC phenotype occurred, this could be advantageous in terms of biocompatibility. Collectively these results indicate that DNA topology is an important parameter for DC vector design, particularly pDNA in the SC conformation in regards to DNA vaccination studies.