Generalized Fractional Calculus, Special Functions and Integral Transforms: What is the Relation?

Виржиния С. Кирякова - В този обзор илюстрираме накратко наши приноси към обобщенията на дробното смятане (анализ) като теория на операторите за интегриране и диференциране от произволен (дробен) ред, на класическите специални функции и на интегралните трансформации от лапласов тип. Показано е, че тези три области на анализа са тясно свързани и взаимно индуцират своето възникване и по-нататъшно развитие. За конкретните твърдения, доказателства и примери, вж. Литературата.

A multiplier theorem for the sublaplacian on the Heisenberg group

A multiplier theorem for the sublaplacian on the Heisenberg group is proved using Littlewood-Paley-Stein theory of g-functions.

Role of the N-terminal region in G protein-coupled receptor functions : negative modulation revealed by 5-HT2B receptor polymorphisms

The putative role of the N-terminal region of rhodopsin-like 7 transmembrane biogenic amine receptors in agonist-induced signaling has not yet been clarified despite recent advances in 7 transmembrane receptor structural biology. Given the existence of N-terminal nonsynonymous polymorphisms (R6G;E42G) within the HTR2B gene in a drug-abusing population, we assessed whether these polymorphisms affect 5-hydroxytryptamine 2B (5-HT2B) receptor in vitro pharmacologic and coupling properties in transfected COS-7 cells. Modification of the 5-HT2B receptor N terminus by the R6G;E42G polymorphisms increases such agonist signaling pathways as inositol phosphate accumulation as assessed by either classic or operational models. The N-terminal R6G;E42G mutations of the 5-HT2B receptor also increase cell proliferation and slow its desensitization kinetics compared with the wild-type receptor, further supporting a role for the N terminus in transduction efficacy. Furthermore, by coexpressing a tethered wild-type 5-HT2B receptor N terminus with a 5-HT2B receptor bearing a N-terminal deletion, we were able to restore original coupling. This reversion to normal activity of a truncated 5-HT2B receptor by coexpression of the membrane-tethered wild-type 5-HT2B receptor N terminus was not observed using a membrane-tethered 5-HT2B receptor R6G;E42G N terminus. These data suggest that the N terminus exerts a negative control over basal as well as agonist-stimulated receptor activity that is lost in the R6G;E42G mutant. Our findings reveal a new and unanticipated role of the 5-HT2B receptor N terminus as a negative modulator, affecting both constitutive and agonist-stimulated activity. Moreover, our data caution against excluding the N terminus and extracellular loops in structural studies of this 7 transmembrane receptor family

Improved quasiparticle wave functions and mean field for G(0)W(0) calculations: Initialization with the COHSEX operator

The GW approximation to the electron self-energy has become a standard method for ab initio calculation of excited-state properties of condensed-matter systems. In many calculations, the G W self-energy operator, E, is taken to be diagonal in the density functional theory (DFT) Kohn-Sham basis within the G0 W0 scheme. However, there are known situations in which this diagonal Go Wo approximation starting from DFT is inadequate. We present two schemes to resolve such problems. The first, which we called sc-COHSEX-PG W, involves construction of an improved mean field using the static limit of GW, known as COHSEX (Coulomb hole and screened exchange), which is significantly simpler to treat than GW W. In this scheme, frequency-dependent self energy E(N), is constructed and taken to be diagonal in the COHSEX orbitals after the system is solved self-consistently within this formalism. The second method is called off diagonal-COHSEX G W (od-COHSEX-PG W). In this method, one does not self-consistently change the mean-field starting point but diagonalizes the COHSEX Hamiltonian within the Kohn-Sham basis to obtain quasiparticle wave functions and uses the resulting orbitals to construct the G W E in the diagonal form. We apply both methods to a molecular system, silane, and to two bulk systems, Si and Ge under pressure. For silane, both methods give good quasiparticle wave functions and energies. Both methods give good band gaps for bulk silicon and maintain good agreement with experiment. Further, the sc-COHSEX-PGW method solves the qualitatively incorrect DFT mean-field starting point (having a band overlap) in bulk Ge under pressure.

G-Quadruplex Aptamers with Peroxidase-Like DNAzyme Functions: Which Is the Best and How Does it Work?

Some G-quadruplex DNA aptamers have been found to strongly bind hemin to form DNAzymes with peroxidase-like activity. To help determine the most suitable DNAzymes and to understand how they work, five previously reported G-quadruplex aptamers were compared for their binding affinity and then the potential catalytic mechanism of their corresponding hemin-G-quadruplex DNAzymes was explored. Among these aptamers, a G-quadruplex named AGRO100 was shown to possess the highest hemin-binding affinity and the best DNAzyme function. This means that AGRO100 is the most ideal candidate for DNAzyme-based analysis. Furthermore, we found the peroxidase-like activity of DNAzyme to be primarily dependent on the concentration of H2O2 and independent of that of the peroxidase substrate (that is, 2,2-azino-bis(3-ethytbenzothiazoline-6-sulfonic acid)diammonium salt). Accordingly, a reaction mechanism for DNAzyme-catalyzed peroxidation is proposed. This study provides new insights into the G-quadruplex-based DNAzymes and will help us to further extend their applications in the analytical field.

Analytical functions for the ground state potential surfaces of C3 (X 1 Σ g+) and HCN (X 1 Σ +)

Analytic functions have been obtained to represent the potential energy surfaces of C3 and HCN in their ground electronic states. These functions closely reproduce the available data on the energy, geometry, and force constants in all stable conformations, as well as data on the various dissociation products, and ab initio calculations of the energy at other conformations. The form of the resulting surfaces are portrayed in various ways and discussed briefly.

Inhibition of G-protein betagamma-subunit functions by phosducin-like protein.

Phosducin is a cytosolic protein predominantly expressed in the retina and the pineal gland that can interact with the betagamma subunits of guanine nucleotide binding proteins (G proteins) and thereby may regulate transmembrane signaling. A cDNA encoding a phosducin-like protein (PhLP) has recently been isolated from rat brain [Miles, M. F., Barhite, S., Sganga, M. & Elliott, M. (1993) Proc. Natl. Acad. Sci. USA 90, 10831-10835. Here we report the expression of PhLP in Escherichia coli and its purification. Recombinant purified PUP inhibited multiple effects of G-protein betagamma subunits. First, it inhibited the betagamma-subunit-dependent ADP-ribosylation of purified alpha(o) by pertussis toxin. Second, it inhibited the GTPase activity of purified G(o). The IC50 value of PhLP in the latter assay was 89 nM, whereas phosducin caused half-maximal inhibition at 17 nM. And finally, PhLP antagonized the enhancement of rhodopsin phosphorylation by purified betagamma subunits. The N terminus of PhLP shows no similarity to the much longer N terminus of phosducin, the region shown to be critical for phosducin-betagamma-subunit interactions. Therefore, PhLP appears to bind to G-protein betagamma subunits by an as yet unknown mode of interaction and may represent an endogenous regulator of G-protein function.

EGCL: an extended G-Code Language with flow control, functions and mnemonic variables

In the context of computer numerical control (CNC) and computer aided manufacturing (CAM), the capabilities of programming languages such as symbolic and intuitive programming, program portability and geometrical portfolio have special importance -- They allow to save time and to avoid errors during part programming and permit code re-usage -- Our updated literature review indicates that the current state of art presents voids in parametric programming, program portability and programming flexibility -- In response to this situation, this article presents a compiler implementation for EGCL (Extended G-code Language), a new, enriched CNC programming language which allows the use of descriptive variable names, geometrical functions and flow-control statements (if-then-else, while) -- Our compiler produces low-level generic, elementary ISO-compliant Gcode, thus allowing for flexibility in the choice of the executing CNC machine and in portability -- Our results show that readable variable names and flow control statements allow a simplified and intuitive part programming and permit re-usage of the programs -- Future work includes allowing the programmer to define own functions in terms of EGCL, in contrast to the current status of having them as library built-in functions

Vitamin D in health and disease : an insight into traditional functions and new roles for the 'sunshine vitamin'

Vitamin D is unique among the vitamins in that humans can synthesize it via the action of UV radiation upon the skin. This combined with its ability to act on specific target tissues via Vitamin D Receptor’s (VDR) make its classification as a steroid hormone more appropriate. While Vitamin D deficiency is a recognized problem in some northern latitude countries, recent studies have shown even in sunny countries such as Australia, vitamin D deficiency may be more prevalent than first thought. Vitamin D is most well known for its role in bone health, however, the discovery of VDR’s on a wide variety of tissue types has also opened up roles for vitamin D far beyond traditional bone health. These include possible associations with autoimmune diseases such as multiple sclerosis and inflammatory bowel diseases, cancer, cardiovascular diseases and muscle strength. Firstly, this paper presents an overview of the two sources of vitamin D: exposure to ultraviolet-B radiation and food sources of vitamin D, with particular focus on both Australian and international studies on dietary vitamin D intake and national fortification strategies. Secondly, the paper reviews recent epidemiological and experimental evidence linking vitamin D and its role in health and disease for the major conditions linked to suboptimal vitamin D, while identifying significant gaps in the research and possible future directions for research.

Differences in the performance of safety performance functions estimated for total crash count and for crash count by crash type

In recent years the development and use of crash prediction models for roadway safety analyses have received substantial attention. These models, also known as safety performance functions (SPFs), relate the expected crash frequency of roadway elements (intersections, road segments, on-ramps) to traffic volumes and other geometric and operational characteristics. A commonly practiced approach for applying intersection SPFs is to assume that crash types occur in fixed proportions (e.g., rear-end crashes make up 20% of crashes, angle crashes 35%, and so forth) and then apply these fixed proportions to crash totals to estimate crash frequencies by type. As demonstrated in this paper, such a practice makes questionable assumptions and results in considerable error in estimating crash proportions. Through the use of rudimentary SPFs based solely on the annual average daily traffic (AADT) of major and minor roads, the homogeneity-in-proportions assumption is shown not to hold across AADT, because crash proportions vary as a function of both major and minor road AADT. For example, with minor road AADT of 400 vehicles per day, the proportion of intersecting-direction crashes decreases from about 50% with 2,000 major road AADT to about 15% with 82,000 AADT. Same-direction crashes increase from about 15% to 55% for the same comparison. The homogeneity-in-proportions assumption should be abandoned, and crash type models should be used to predict crash frequency by crash type. SPFs that use additional geometric variables would only exacerbate the problem quantified here. Comparison of models for different crash types using additional geometric variables remains the subject of future research.

Integration-segregation decisions under general value functions: "create your own bundle - choose 1, 2, or all 3!",

Whether to keep products segregated (e.g., unbundled) or integrate some or all of them (e.g., bundle) has been a problem of profound interest in areas such as portfolio theory in finance, risk capital allocations in insurance and marketing of consumer products. Such decisions are inherently complex and depend on factors such as the underlying product values and consumer preferences, the latter being frequently described using value functions, also known as utility functions in economics. In this paper, we develop decision rules for multiple products, which we generally call ‘exposure units’ to naturally cover manifold scenarios spanning well beyond ‘products’. Our findings show, e.g. that the celebrated Thaler's principles of mental accounting hold as originally postulated when the values of all exposure units are positive (i.e. all are gains) or all negative (i.e. all are losses). In the case of exposure units with mixed-sign values, decision rules are much more complex and rely on cataloging the Bell number of cases that grow very fast depending on the number of exposure units. Consequently, in the present paper, we provide detailed rules for the integration and segregation decisions in the case up to three exposure units, and partial rules for the arbitrary number of units.

Mass spectrometry-based metabolomics towards understanding of gene functions with a diversity of biological contexts

Currently, mass spectrometry-based metabolomics studies extend beyond conventional chemical categorization and metabolic phenotype analysis to understanding gene function in various biological contexts (e.g., mammalian, plant, and microbial). These novel utilities have led to many innovative discoveries in the following areas: disease pathogenesis, therapeutic pathway or target identification, the biochemistry of animal and plant physiological and pathological activities in response to diverse stimuli, and molecular signatures of host-pathogen interactions during microbial infection. In this review, we critically evaluate the representative applications of mass spectrometry-based metabolomics to better understand gene function in diverse biological contexts, with special emphasis on working principles, study protocols, and possible future development of this technique. Collectively, this review raises awareness within the biomedical community of the scientific value and applicability of mass spectrometry-based metabolomics strategies to better understand gene function, thus advancing this application's utility in a broad range of biological fields

Gemcitabine reactivates epigenetically silenced genes and functions as a DNA methyltransferase inhibitor

Gemcitabine is indicated in combination with cisplatin as first-line therapy for solid tumours including non-small cell lung cancer (NSCLC), bladder cancer and mesothelioma. Gemcitabine is an analogue of pyrimidine cytosine and functions as an anti-metabolite. Structurally, however, gemcitabine has similarities to 5-aza-2-deoxycytidine (decitabine/Dacogen®), a DNA methyltransferase inhibitor (DNMTi). NSCLC, mesothelioma and prostate cancer cell lines were treated with decitabine and gemcitabine. Reactivation of epigenetically silenced genes was examined by RT-PCR/qPCR. DNA methyltransferase activity in nuclear extracts and recombinant proteins was measured using a DNA methyltransferase assay, and alterations in DNA methylation status were examined using methylation-specific PCR (MS-PCR) and pyrosequencing. We observe a reactivation of several epigenetically silenced genes including GSTP1, IGFBP3 and RASSF1A. Gemcitabine functionally inhibited DNA methyltransferase activity in both nuclear extracts and recombinant proteins. Gemcitabine dramatically destabilised DNMT1 protein. However, DNA CpG methylation was for the most part unaffected by gemcitabine. In conclusion, gemcitabine both inhibits and destabilises DNA methyltransferases and reactivates epigenetically silenced genes having activity equivalent to decitabine at concentrations significantly lower than those achieved in the treatment of patients with solid tumours. This property may contribute to the anticancer activity of gemcitabine.

Distinguishing between mechanisms of cell aggregation using pair-correlation functions

Many cell types form clumps or aggregates when cultured in vitro through a variety of mechanisms including rapid cell proliferation, chemotaxis, or direct cell-to-cell contact. In this paper we develop an agent-based model to explore the formation of aggregates in cultures where cells are initially distributed uniformly, at random, on a two-dimensional substrate. Our model includes unbiased random cell motion, together with two mechanisms which can produce cell aggregates: (i) rapid cell proliferation, and (ii) a biased cell motility mechanism where cells can sense other cells within a finite range, and will tend to move towards areas with higher numbers of cells. We then introduce a pair-correlation function which allows us to quantify aspects of the spatial patterns produced by our agent-based model. In particular, these pair-correlation functions are able to detect differences between domains populated uniformly at random (i.e. at the exclusion complete spatial randomness (ECSR) state) and those where the proliferation and biased motion rules have been employed - even when such differences are not obvious to the naked eye. The pair-correlation function can also detect the emergence of a characteristic inter-aggregate distance which occurs when the biased motion mechanism is dominant, and is not observed when cell proliferation is the main mechanism of aggregate formation. This suggests that applying the pair-correlation function to experimental images of cell aggregates may provide information about the mechanism associated with observed aggregates. As a proof of concept, we perform such analysis for images of cancer cell aggregates, which are known to be associated with rapid proliferation. The results of our analysis are consistent with the predictions of the proliferation-based simulations, which supports the potential usefulness of pair correlation functions for providing insight into the mechanisms of aggregate formation.

Shrinking the keys of discrete-log-type lossy trapdoor functions

To this day, realizations in the standard-model of (lossy) trapdoor functions from discrete-log-type assumptions require large public key sizes, e.g., about Θ(λ 2) group elements for a reduction from the decisional Diffie-Hellman assumption (where λ is a security parameter). We propose two realizations of lossy trapdoor functions that achieve public key size of only Θ(λ) group elements in bilinear groups, with a reduction from the decisional Bilinear Diffie-Hellman assumption. Our first construction achieves this result at the expense of a long common reference string of Θ(λ 2) elements, albeit reusable in multiple LTDF instantiations. Our second scheme also achieves public keys of size Θ(λ), entirely in the standard model and in particular without any reference string, at the cost of a slightly more involved construction. The main technical novelty, developed for the second scheme, is a compact encoding technique for generating compressed representations of certain sequences of group elements for the public parameters.