Fuzzy tori are finite dimensional C*-algebras endowed with an appropriate notion of noncommutative geometry inherited from ergodic action a closed subgroup the torus, which meant as approximations and more generally, quantum tori. A mean to specify space is by constructing over it spectral triple. We prove in this paper that we can construct triples on fuzzy which, dimension grows infinity unde...

After arguing why the Batalin–Vilkovisky (BV) formalism is expected to find a natural description within framework of noncommutative geometry, we explain how this relation takes form for gauge theories induced by finite spectral triples. In particular, demonstrate two extension procedures appearing in BV formalism, that is, initial via introduction ghost/anti-ghost fields and further with auxil...

A multimodal methodology for spectral imaging of cells is presented. The spectral imaging setup uses a transmission diffraction grating on a light microscope to concurrently record spectral images of cells and cellular organelles by fluorescence, darkfield, brightfield, and differential interference contrast (DIC) spectral microscopy. Initially, the setup was applied for fluorescence spectral i...

Callias-type (or Dirac-Schrödinger) operators associated to abstract semifinite spectral triples are introduced and their indices computed in terms of an index pairing derived from the triple. The result is then interpreted as theorem for a non-commutative analogue flow. Both even odd considered, both commutative examples given.

To exploit hyperspectral image's (HSI) spectral-spatial information and reduce network complexity, a triple path convolution neural (CNN) with interleave-attention mechanism is constructed for high-precision classification. A hybrid branch proposed to capture joint features, which are later utilized as complementary purely spectral spatial features. Furthermore, the elaborately designed ...

We develop (within a possibly new) framework spectral analysis and operator theory on (almost) general graphs and use it to study spectral properies of the graph-Laplacian and so-called graph-Dirac-operators. That is, we introduce a Hilbert space structure, being in our framework the direct sum of a node-Hilbert-space and a bond-Hilbert-space, a Dirac operator intertwining these components, and...

The product of two real spectral triples {A1,H1,D1,J1, γ1} and {A2,H2,D2,J2(, γ2)}, the first of which is necessarily even, was defined by A.Connes [3] as {A,H,D,J (, γ)} given by A = A1 ⊗ A2, H = H1 ⊗ H2, D = D1 ⊗ Id2 + γ1 ⊗ D2, J = J1 ⊗ J2 and, in the even-even case, by γ = γ1⊗γ2. Generically it is assumed that the real structure J obeys the relations J 2 = ǫId, JD = ǫ ′DJ , J γ = ǫ ′′γJ , wh...

We develop a graph-Hilbert-space framework, inspired by non-commutative geometry, on (infinite) graphs and use it to study spectral properies of graph-Laplacians and so-called graph-Dirac-operators. Putting the various pieces together we define a spectral triplet sharing most (if not all, depending on the particular graph model) of the properties of what Connes calls a spectral triple. With the...

Given an expansive matrix R ∈ Md(ℤ) and a finite set of digit B taken from ℤd/R(ℤd). It was shown previously that if we can find L such (R, B, L) forms Hadamard triple, then the associated fractal self-affine measure generated by B) admits exponential orthonormal basis certain frequency Λ, hence it is termed as spectral measure. In this paper, show #B < ∣det(R)∣, not only spectral, also constru...