Elemental t.g. Principles of Relativistic t-Topos (Presheafification of Matter, Space, and Time)

We would like to solve the following problem: find a mathematical model formulating I) quantum entanglement, II) particle-wave duality, III) universal objects (ur-sub-Planck objects): to be defined in terms of direct or inverse limits (defined by universal mapping properties) giving microcosm behaviors of space-time so as to give the smooth macrocosm space-time, and IV) the “curved” space-time associated with particles with mass in microcosm consistent with the notion of a light cone in macrocosm. Problems I) and II) are treated in Kato G., Europhys. Lett., 68 (2004) 467. In this paper, we will focus on III) and IV). As a candidate for such a model, we have introduced the category of presheaves over a site called a t-topos. During the last several years, the methods of category and sheaf theoretic approaches have been actively employed for the foundations of quantum physics and for quantum gravity. Particles, time, and space are presheafified in the following sense: a fundamental entity is a triple (m, κ, τ ) of presheaves so that for an object V in a t-site, a local datum (m(V ), κ(V ), τ(V )) may provide a local state of the particle m_ = m(V), i.e., the localization of presheaf m at V , in the neighborhood (κ(V ), τ(V )) of m_. By presheafifying matter, space, and time, t-topos can provide sheaf-theoretic descriptions of ur-entanglement and ur-particle and ur-wave states(1) formul ating the EPR-type non-locality and the duality in a double-slit experiment. Recall that presheaves m and m\u27 are said to be ur-entangled when m and m\u27 behave as one presheaf. Also recall: a presheaf m is said to be in particle ur-state (or wave ur-state) when the presheaf m is evaluated as m(V ) at a specified object V in the t-site (or when an object in the t-site is not specified). For more comments and the precise definitions of ur-entanglement and particle and wave ur-states, see the above-mentioned paper. The applications to a double-slit experiment and the EPR-type non-locality are described in detail in the forthcoming papers Kato G. and Tanaka T., Double slit experiment and t-topos, submitted to Found. Phys. and Kafatos M., Kato G., Roy S. and Tanaka T., The EPR-type non-locality and t-topos, to be submitted to Int. J. Pure Appl. Math., respectively. By the notion of decompositions of a presheaf and of an object of the t-site, ur-sub-Planck objects are defined as direct and inverse limits, respectively, in Definitions 2.1 and 2.4 in what will follow

\u3cem\u3eu\u3c/em\u3e-Singularity and \u3cem\u3et\u3c/em\u3e-Topos Theoretic Entropy

We will give descriptions of u-singularities as we introduce the notion of t-topos theoretic entropies. The unifying methodology for a u-singularity is the universal mapping property of an inverse or direct limit. The qualitative, conceptual, and structural analyses of u-singularities are given in terms of inverse and direct limits of micro decompositions of a presheaf and coverings of an object in t-site in the theory of temporal topos

Double-Slit Interference and Temporal Topos

The electron double-slit interference is re-examined from the point of view of temporal topos. Temporal topos (or t-topos) is an abstract algebraic (categorical) method using the theory of sheaves. A brief introduction to t-topos is given. When the structural foundation for describing particles is based on t-topos, the particle-wave duality of electron is a natural consequence. A presheaf associated with the electron represents both particle-like and wave-like properties depending upon whether an object in the site (t-site) is specified (particle-like) or not (wave-like). It is shown that the localization of the electron at one of the slits is equivalent to choosing a particular object in the t-site and that the electron behaves as a wave when it passes through a double-slit because there are more than one object in the t-site. Also, the single-slit diffraction is interpreted as a result of the possibility of many different ways of factoring a morphism between two objects

Sheaf Theoretic Formulation for Consciousness and Qualia and Relationship to the Idealism of Non-Dual Philosophies

Questions about the nature of reality, whether Consciousness is the fundamental reality in the universe, and what is Consciousness itself, have no answer in systems that assume an external reality independent of Consciousness. Ultimately, the ontological foundation of such systems is the absolute division of subject and object. We advocate instead what we consider to be an approach that is in agreement with the foundation of quantum reality, which is based on Rāmānuja’s version of Vedanta philosophy and non-dual Kashmir Śaivism. Quantum mechanics opened the door to consciousness, but it cannot account for consciousness. However, the quantum measurement problem implies that we cannot remove subjective experience from the practice of science. It is then appropriate to seek mathematical formalisms for the workings of consciousness that don’t rely on specific interpretations of quantum mechanics. Temporal topos provides such a framework. In the theory of temporal topos, which we outline here, the difference between a subject and an object involves the direction of a morphism in a category. We also note that in the dual category, the direction of the morphism is in the opposite direction compared with the original direction of the original category. The resulting formalism provides powerful ways to address consciousness and qualia, beyond attempts to account for consciousness through physical theories. We also discuss the implications of the mathematics presented here for the convergence of science and non-dualist philosophies, as an emerging science of Consciousness, that may bring out the underlying unity of physics, life and mind

A Sheaf Theoretic Approach to Consciousness

A new fundamental mathematical model of consciousness based on category theory is presented. The model is based on two philosophical-theological assumptions: a) the universe is a sea of consciousness, and b) time is multi-dimensional and non-linear

Sheaf Cohomology and Geometrical Approach to EPR Non-locality

A consistent geometrical approach to EPR non-locality as well as other non-local effects in QM like the Aharanov-Bohm effect, Berry phase, Gauge theories within Yang-Mills theory etc. is possible within the framework of sheaf cohomology. This sheds new light on our understanding on non-local correlations in QM, and provides a fundamental mathematical approach to fundamental problems in physics.Comment: pdf file, 10 page

Purification, molecular cloning and functional characterization of flavonoid C-glucosyltransferases from Fagopyrum esculentum M. (buckwheat) cotyledon

C-Glycosides are characterized by their C-C bonds in which the anomeric carbon of the sugar moieties is directly bound to the carbon atom of aglycon. C-Glycosides are remarkably stable, as their C-C bonds are resistant to glycosidase or acid hydrolysis. A variety of plant species are known to accumulate C-glycosylflavonoidshowever, the genes encoding for enzymes that catalyze C-glycosylation of flavonoids have been identified only from Oryza sativa (rice) and Zea mays (maize), and have not been identified from dicot plants. In this study, we identified the C-glucosyltransferase gene from the dicot plant Fagopyrum esculentumM. (buckwheat). We purified two isozymes from buckwheat seedlings that catalyze C-glucosylation of 2-hydroxyflavanones, which are expressed specifically in the cotyledon during seed germination. Following purification we isolated the cDNA corresponding to each isozyme [FeCGTa (UGT708C1) and FeCGTb (UGT708C2)]. When expressed in Escherichia coli, both proteins demonstrated C-glucosylation activity towards 2-hydroxyflavanones, dihydrochalcone, trihydroxyacetophenones and other related compounds with chemical structures similar to 2,4,6-trihydroxyacetophenone. Molecular phylogenetic analysis of plant glycosyltransferases shows that flavonoid C-glycosyltransferases form a different clade with other functionally analyzed plant glycosyltransferases.ArticlePLANT JOURNAL. 80(3):437-448 (2014)journal articl

Isolation of genes coding for chitin-degrading enzymes in the novel chitinolytic bacterium, Chitiniphilus shinanonensis, and characterization of a gene coding for a family 19 chitinase

Chitiniphilus shinanonensis type strain SAY3(T) is a strongly chitinolytic bacterium, originally isolated from the moat water in Ueda, Japan. To elucidate the chitinolytic activity of this strain, 15 genes (chiA-chiO) coding for putative chitin-degrading enzymes were isolated from a genomic library. Sequence analysis revealed the genes comprised 12 family 18 chitinases, a family 19 chitinase, a family 20 beta-N-acetylglucosaminidase, and a polypeptide with a chitin-binding domain but devoid of a catalytic domain. Two operons were detected among the sequences: chiCDEFG and chiLM. The gene coding for the polypeptide (chiN) showed sequence similarity to family 19 chitinases and was successfully expressed in Escherichia colt. ChiN demonstrated a multi-domain structure, composed of the N-terminal, two chitin-binding domains connected by a Pro- and Thr-rich linker, and a family 19 catalytic domain located at the C-terminus. The recombinant protein rChiN catalyzed an endo-type cleavage of N-acetyl-D-glucosamine oligomers, and also degraded insoluble chitin and soluble chitosan (degree of deacetylation of 80%). rChiN exhibited an inhibitory effect on hyphal growth of the fungus Trichoderma reesei. The chitin-binding domains of ChiN likely play an important role in the degradation of insoluble chitin, and are responsible for a growth inhibitory effect on fungi. (C) 2011, The Society for Biotechnology, Japan. All rights reserved.ArticleJOURNAL OF BIOSCIENCE AND BIOENGINEERING. 113(3):293-299 (2012)journal articl

Distribution and Endocrine Morphology of Polypeptide YY (PYY) Containing Cells in the Human Gut

Using human materials, the distribution of PYY containing cells was determined by immunocytochemical methods and discussion was made on their morphological endocrinology. PYY cells were fairly numerous in the lower gastrointestinal tract of man, particularly in the colon and rectum. The cells were also present in the pancreas and duodenum but quite rarely. PYY cells were not observed at all in the lower part of the esophagus, stomach and gall bladder. Their peculiar and characteristic shapes as well as distribution suggest that PYY may have some action (probably specific) on the function of the distal gastrointestinal tract

Long-term results of the open stent-grafting technique for extended aortic arch disease

ObjectiveThis report elucidates the long-term safety and effectiveness of extended aortic arch replacement with an open stent-grafting technique from our 12 years of experience.MethodsFrom 1994 to 2004, 126 patients (mean age 67.8 years) with different pathologic conditions of the aortic arch with extension to the descending aorta (57 dissections [acute/chronic = 31/26] and 69 aneurysms) were operated on with an open stent-grafting technique. During deep hypothermic circulatory arrest with selective cerebral perfusion, the stent graft was delivered through the transected proximal aortic arch, and arch replacement with a 4-branched prosthesis was performed.ResultsOperative mortality within 30 days was 3.2%. Perioperative morbidity included 7 (5.6%) strokes and 8 (6.3%) spinal injuries (paraplegia in 3, transient paraparesis in 5). Sixty-three percent of the patients were extubated within 24 hours. In long-term follow-up (mean 60.4 ± 36.5 months, maximum 153 months), survival was 81.1%, 63.3%, and 53.7% at 1, 5, and 8 years. Five (3.9%) late endoleaks were observed but treated with successful additional endovascular repair. Freedom from endoleaks was 98.0%, 91.1%, and 91.1% for 1, 5, and 8 years, respectively.ConclusionLong-term observation showed safety and good durability of the open stent-grafting technique for aortic arch disease. This technique could be an attractive treatment option for aortic arch aneurysm with distal extension and aortic dissection requiring aortic arch replacement