A Sheaf Model of the Algebraic Closure

In constructive algebra one cannot in general decide the irreducibility of a polynomial over a field K. This poses some problems to showing the existence of the algebraic closure of K. We give a possible constructive interpretation of the existence of the algebraic closure of a field in characteristic 0 by building, in a constructive metatheory, a suitable site model where there is such an algebraic closure. One can then extract computational content from this model. We give examples of computation based on this model.Comment: In Proceedings CL&C 2014, arXiv:1409.259

Nanoparticle-based capillary electrochromatography

In this work, lipid nanoparticles were used as pseudostationary phase, PSP, for protein separation in capillary electrochromatography, CEC. The aim of the work was to use a new analytical separation technique for future analysis of protein drugs by using lipid nanoparticles as a pseudo-stationary phase with conventional UV-detection. PSP-CEC was combined with UV-detection to study proteins elution. The tested proteins BSA, cytochrome c and insulin have been selected according to different hydrophobicities, sizes and isoelectric points (pI). A zwitter ionic buffer, MOPS, was used as an electrolyte at pH 7.4. The nanoparticles were tested for their compatibility with MALDI-TOF/MS (Matrix assisted laser desorption/ionization-time of flight). MADI-TOF/MS works with a suspension of lipid nanoparticles in MOPS that contains insulin and it can be a future possible detection method for PSP-CEC. All three proteins were successfully eluted with PSP-CEC combined with UV-detection. Nanoparticles coated with silver might be studied with “surface enhanced Raman spectroscopy”-detection.Popular Science Summery Capillary electrophoresis, CE is a separation technique in which analytes are separated according to their size to charge ratio in the interior of the capillary. Capillary electrochromatography, CEC is a combination of CE and HPLC. The fundamental difference between CE and CEC is that the separation is not based on the electrophoretic mobility difference only but on the interaction with the stationary phase as well. Lipid nanoparticles were used as pseudostationary phase (moving phase). The aim of current work is to separate different proteins, BSA, cytochrome c and insulin have been separated according to their charge and size. They have been successfully separated. It was found that PSP-CEC in combination with UV-detection is a good methodology to elute Proteins. An identification technique named MALDI-TOF/MS was used to identify the insulin that has been dissolved in nanoparticles. Insulin has been successfully identified. MADI-TOF/MS works well with lipid nanoparticles and it can be used as a future possible detection of PSP-CEC

The Independence of Markov's Principle in Type Theory

In this paper, we show that Markov's principle is not derivable in dependent type theory with natural numbers and one universe. One way to prove this would be to remark that Markov's principle does not hold in a sheaf model of type theory over Cantor space, since Markov's principle does not hold for the generic point of this model. Instead we design an extension of type theory, which intuitively extends type theory by the addition of a generic point of Cantor space. We then show the consistency of this extension by a normalization argument. Markov's principle does not hold in this extension, and it follows that it cannot be proved in type theory

Dynamic Newton-Puiseux Theorem

A constructive version of Newton-Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization algorithm of polynomials over the base field is not needed. The extensions obtained are a type of regular algebras over the base field and the expansions are given as formal power series over these algebras.Comment: 22 pag

The Clocks They Are Adjunctions: Denotational Semantics for Clocked Type Theory

Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract form of step-indexing. CloTT has previously been shown to enjoy a number of syntactic properties including strong normalisation, canonicity and decidability of type checking. In this paper we present a denotational semantics for CloTT useful, e.g., for studying future extensions of CloTT with constructions such as path types. The main challenge for constructing this model is to model the notion of ticks used in CloTT for coinductive reasoning about coinductive types. We build on a category previously used to model guarded recursion, but in this category there is no object of ticks, so tick-assumptions in a context can not be modelled using standard tools. Instead we show how ticks can be modelled using adjoint functors, and how to model the tick constant using a semantic substitution

Stack semantics of type theory

We give a model of dependent type theory with one univalent universe and propositional truncation interpreting a type as a stack, generalising the groupoid model of type theory. As an application, we show that countable choice cannot be proved in dependent type theory with one univalent universe and propositional truncation

Ticking clocks as dependent right adjoints: Denotational semantics for clocked type theory

Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract form of step-indexing. CloTT has previously been shown to enjoy a number of syntactic properties including strong normalisation, canonicity and decidability of the equational theory. In this paper we present a denotational semantics for CloTT useful, e.g., for studying future extensions of CloTT with constructions such as path types. The main challenge for constructing this model is to model the notion of ticks on a clock used in CloTT for coinductive reasoning about coinductive types. We build on a category previously used to model guarded recursion with multiple clocks. In this category there is an object of clocks but no object of ticks, and so tick-assumptions in a context can not be modelled using standard tools. Instead we model ticks using dependent right adjoint functors, a generalisation of the category theoretic notion of adjunction to the setting of categories with families. Dependent right adjoints are known to model Fitch-style modal types, but in the case of CloTT, the modal operators constitute a family indexed internally in the type theory by clocks. We model this family using a dependent right adjoint on the slice category over the object of clocks. Finally we show how to model the tick constant of CloTT using a semantic substitution. This work improves on a previous model by the first two named authors which not only had a flaw but was also considerably more complicated.Comment: 31 pages. Second version is a minor revision. arXiv admin note: text overlap with arXiv:1804.0668

Neuroprotective role of vitamin D3 in colchicine-induced Alzheimer’s disease in rats

Background: Alzheimer’s disease (AD) is a complex neurodegenerative disease characterized by progressive decline in memory, language and other cognitive functions. Recent studies provide convincing evidence on the role of vitamin D3 on the nervous system.Aim: To investigate the effect of the active form of vitamin D3 (1,25-dihydroxycholecalciferol) as a neuroprotective agent in experimentally induced AD in rats.Methods: 40 adult male Wistar (albino) rats weighing 180 to 200 g were included in this study. Rats were divided into four groups (each of 10 rats): Group I: normal healthy rats receiving intracerebroventricular injection (icv) of artificial cerebrospinal fluid (ACSF) and serving as a control group. Group II: rats with induced AD by icv colchicine injection of 15 lg/rat bilaterally and receiving no treatment. Group III: rats pre-treated with active form of vitamin D3 42 IU/kg/day subcutaneously (s.c.) for one week followed by induction of AD then post-treated with vitamin D3 in the same dose for 3 weeks. Group IV: rats with induced AD then post-treated with vitamin D3 for 3 weeks. The following parameters were evaluated in rats of all studied groups1- Behavioral assessment: Morris water maze and open field tasks were performed at days   13, 14 and 21 post-icv injection for assessing cognitive, gross behavioral and motor activities of studied groups.2- Biochemical tests: Hippocampal tissue levels of brain derived neurotrophic factor (BDNF), amyloid beta (Ab) peptide, and antioxidant system; glutathione reductase (GR) and glutathione peroxidase (GPX).Results: The present study revealed a significant increase in time latency of water maze test and hippocampal tissue level of Ab peptide concomitant with significant reduction of hippocampal tissue levels of BDNF, GR and GPX, in untreated AD rats (group II) versus control ACSF-injected rats (group I) and vitamin D3-treated AD rats (groups III and IV). However, group III (AD rats pre- and post-treated with vitamin D3) showed a significant decrease in time latency and Ab peptide, and a significant elevation of BDNF, GR and GPX, versus group IV (AD rats post-treated with vitamin D3).Conclusion: Prophylactic use of active form of vitamin D3 (1,25(OH)2D3) appears to possess a neuroprotective effect in AD involving various mechanisms. Hence, vitamin D3 or its analogues can be considered as promising agents for development of new prophylactic and therapeutic neuroprotectors