241 research outputs found
Calculating Colimits Compositionally
We show how finite limits and colimits can be calculated compositionally
using the algebras of spans and cospans, and give as an application a proof of
the Kleene Theorem on regular languages
Comparison of high-specific-activity ultratrace 123/131I-MIBG and carrier-added 123/131I-MIBG on efficacy, pharmacokinetics, and tissue distribution
Metaiodobenzylguanidine (MIBG) is an enzymatically stable synthetic analog of norepinephrine that when radiolabled with diagnostic ((123)I) or therapeutic ((131)I) isotopes has been shown to concentrate highly in sympathetically innervated tissues such as the heart and neuroendocrine tumors that possesses high levels of norepinephrine transporter (NET). As the transport of MIBG by NET is a saturable event, the specific activity of the preparation may have dramatic effects on both the efficacy and safety of the radiodiagnostic/radiotherapeutic. Using a solid labeling approach (Ultratrace), noncarrier-added radiolabeled MIBG can be efficiently produced. In this study, specific activities of >1200 mCi/micromol for (123)I and >1600 mCi/micromol for (131)I have been achieved. A series of studies were performed to assess the impact of cold carrier MIBG on the tissue distribution of (123/131)I-MIBG in the conscious rat and on cardiovascular parameters in the conscious instrumented dog. The present series of studies demonstrated that the carrier-free Ultratrace MIBG radiolabeled with either (123)I or (131)I exhibited similar tissue distribution to the carrier-added radiolabeled MIBG in all nontarget tissues. In tissues that express NETs, the higher the specific activity of the preparation the greater will be the radiopharmaceutical uptake. This was reflected by greater efficacy in the mouse neuroblastoma SK-N-BE(2c) xenograft model and less appreciable cardiovascular side-effects in dogs when the high-specific-activity radiopharmaceutical was used. The increased uptake and retention of Ultratrace (123/131)I-MIBG may translate into a superior diagnostic and therapeutic potential. Lastly, care must be taken when administering therapeutic doses of the current carrier-added (131)I-MIBG because of its potential to cause adverse cardiovascular side-effects, nausea, and vomiting
Nets, relations and linking diagrams
In recent work, the author and others have studied compositional algebras of
Petri nets. Here we consider mathematical aspects of the pure linking algebras
that underly them. We characterise composition of nets without places as the
composition of spans over appropriate categories of relations, and study the
underlying algebraic structures.Comment: 15 pages, Proceedings of 5th Conference on Algebra and Coalgebra in
Computer Science (CALCO), Warsaw, Poland, 3-6 September 201
On Gammelgaard's formula for a star product with separation of variables
We show that Gammelgaard's formula expressing a star product with separation
of variables on a pseudo-Kaehler manifold in terms of directed graphs without
cycles is equivalent to an inversion formula for an operator on a formal Fock
space. We prove this inversion formula directly and thus offer an alternative
approach to Gammelgaard's formula which gives more insight into the question
why the directed graphs in his formula have no cycles.Comment: 29 pages, changes made in the last two section
Reproducibility of the heat/capsaicin skin sensitization model in healthy volunteers
INTRODUCTION: Heat/capsaicin skin sensitization is a well-characterized human experimental model to induce hyperalgesia and allodynia. Using this model, gabapentin, among other drugs, was shown to significantly reduce cutaneous hyperalgesia compared to placebo. Since the larger thermal probes used in the original studies to produce heat sensitization are now commercially unavailable, we decided to assess whether previous findings could be replicated with a currently available smaller probe (heated area 9 cm(2) versus 12.5â15.7 cm(2)). STUDY DESIGN AND METHODS: After Institutional Review Board approval, 15 adult healthy volunteers participated in two study sessions, scheduled 1 week apart (Part A). In both sessions, subjects were exposed to the heat/capsaicin cutaneous sensitization model. Areas of hypersensitivity to brush stroke and von Frey (VF) filament stimulation were measured at baseline and after rekindling of skin sensitization. Another group of 15 volunteers was exposed to an identical schedule and set of sensitization procedures, but, in each session, received either gabapentin or placebo (Part B). RESULTS: Unlike previous reports, a similar reduction of areas of hyperalgesia was observed in all groups/sessions. Fading of areas of hyperalgesia over time was observed in Part A. In Part B, there was no difference in area reduction after gabapentin compared to placebo. CONCLUSION: When using smaller thermal probes than originally proposed, modifications of other parameters of sensitization and/or rekindling process may be needed to allow the heat/capsaicin sensitization protocol to be used as initially intended. Standardization and validation of experimental pain models is critical to the advancement of translational pain research
Combinatorial Hopf algebras and Towers of Algebras
Bergeron and Li have introduced a set of axioms which guarantee that the
Grothendieck groups of a tower of algebras can be
endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap,
and independently Lam and Shimozono constructed dual graded graphs from
primitive elements in Hopf algebras. In this paper we apply the composition of
these constructions to towers of algebras. We show that if a tower
gives rise to graded dual Hopf algebras then we must
have where .Comment: 7 page
Reverse Bisimulations on Stable Configuration Structures
The relationships between various equivalences on configuration structures,
including interleaving bisimulation (IB), step bisimulation (SB) and hereditary
history-preserving (HH) bisimulation, have been investigated by van Glabbeek
and Goltz (and later Fecher). Since HH bisimulation may be characterised by the
use of reverse as well as forward transitions, it is of interest to investigate
forms of IB and SB where both forward and reverse transitions are allowed. We
give various characterisations of reverse SB, showing that forward steps do not
add extra power. We strengthen Bednarczyk's result that, in the absence of
auto-concurrency, reverse IB is as strong as HH bisimulation, by showing that
we need only exclude auto-concurrent events at the same depth in the
configuration
Three qubit entanglement within graphical Z/X-calculus
The compositional techniques of categorical quantum mechanics are applied to
analyse 3-qubit quantum entanglement. In particular the graphical calculus of
complementary observables and corresponding phases due to Duncan and one of the
authors is used to construct representative members of the two genuinely
tripartite SLOCC classes of 3-qubit entangled states, GHZ and W. This nicely
illustrates the respectively pairwise and global tripartite entanglement found
in the W- and GHZ-class states. A new concept of supplementarity allows us to
characterise inhabitants of the W class within the abstract diagrammatic
calculus; these method extends to more general multipartite qubit states.Comment: In Proceedings HPC 2010, arXiv:1103.226
The fundamental pro-groupoid of an affine 2-scheme
A natural question in the theory of Tannakian categories is: What if you
don't remember \Forget? Working over an arbitrary commutative ring , we
prove that an answer to this question is given by the functor represented by
the \'etale fundamental groupoid \pi_1(\spec(R)), i.e.\ the separable
absolute Galois group of when it is a field. This gives a new definition
for \'etale \pi_1(\spec(R)) in terms of the category of -modules rather
than the category of \'etale covers. More generally, we introduce a new notion
of "commutative 2-ring" that includes both Grothendieck topoi and symmetric
monoidal categories of modules, and define a notion of for the
corresponding "affine 2-schemes." These results help to simplify and clarify
some of the peculiarities of the \'etale fundamental group. For example,
\'etale fundamental groups are not "true" groups but only profinite groups, and
one cannot hope to recover more: the "Tannakian" functor represented by the
\'etale fundamental group of a scheme preserves finite products but not all
products.Comment: 46 pages + bibliography. Diagrams drawn in Tik
Correlating matched-filter model for analysis and optimisation of neural networks
A new formalism is described for modelling neural networks by means of which a clear physical understanding of the network behaviour can be gained. In essence, the neural net is represented by an equivalent network of matched filters which is then analysed by standard correlation techniques. The procedure is demonstrated on the synchronous Little-Hopfield network. It is shown how the ability of this network to discriminate between stored binary, bipolar codes is optimised if the stored codes are chosen to be orthogonal. However, such a choice will not often be possible and so a new neural network architecture is proposed which enables the same discrimination to be obtained for arbitrary stored codes. The most efficient convergence of the synchronous Little-Hopfield net is obtained when the neurons are connected to themselves with a weight equal to the number of stored codes. The processing gain is presented for this case. The paper goes on to show how this modelling technique can be extended to analyse the behaviour of both hard and soft neural threshold responses and a novel time-dependent threshold response is described
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