For an arbitrary self-adjoint operator $B$ in a Hilbert space $H$, we present direct and inverse theorems establishing the relationship between the degree of smoothness of a vector $x \in H$ with respect to the operator $B$, the rate of convergence...
Brain fiber tracts are widely used in studying brain diseases, which may lead to a better understanding of how disease affects the brain. The segmentation of brain fiber tracts assumed enormous importance in disease analysis. In this paper, we propos...
This paper proves a linear algebra result that has to do with the geometry of "widgets". For us a widget is a collection of n pairs of points in a vector space. (The pairs represent the different possible spin states of a particle.) We investigate li...
A Mall bundle on a Hopf manifold H is a holomorphic vector bundle whose pullback to the universal cover of H is trivial. We define resonant and non-resonant Mall bundles, generalizing the notion of the resonance in ODE, and prove that a non-resonant...
A geometric version of the Poincaré Lemma is established for the topological vector space of differential chains. In particular, every differential k-cycle with compact support in a contractible open subset U of a smooth n-manifold M is the boundary...
I'm in Linear Algebra right now and we're mostly just working with vector spaces, but they're introducing us to the basic concepts of fields and groups in preparation taking for Abstract Algebra la...
Gather/scatter is a type of memory addressing that at once collects (gathers) from, or stores (scatters) data to, multiple arbitrary memory indices. Examples
A plotter is a machine that produces vector graphics drawings. Plotters draw lines on paper using a pen, or in some applications, use a knife to cut a
?️?Create, Customize and Talk to your AI Character/Companion in Realtime (All in One Codebase!). Have a natural seamless conversation with AI everywhere (mobile, web and terminal) using LLM OpenAI GPT3.5/4, Anthropic Claude2, Chroma Vector DB, Whisper Speech2T…
MicroCanvas is a 2D Graphics Engine built for ESP32 to make portable GUI, Video Games, Vector Graphics for any display. You can add support for any display in port layer. Contributions are always welcome :) (⭐ 56)
This work adapts two recent architectures of generative models and evaluates their effectiveness for the conversion of whispered speech to normal speech. We incorporate the normal target speech into the training criterion of vector-quantized variatio...
Solitons, as stable localized wave packets that can propagate long distance in dispersive media without changing their shapes, are ubiquitous in nonlinear physical systems. Since the first experimental realization of optical bright solitons in the an...
We study the theta decomposition of Jacobi forms of nonintegral lattice index for a representation that arises in the theory of Weil representations associated to even lattices, and suggest possible applications....
We construct a nontrivial cyclic cocycle on the Weyl algebra of a symplectic vector space. Using this cyclic cocycle we construct an explicit, local, quasi-isomorphism from the complex of differential forms on a symplectic manifold to the complex o...
We introduce higher analogs for cleavages in the context of (Kan) simplicial fibrations. We apply them to obtain geometric models for representations up to homotopy of (higher) Lie groupoids. Concretely, we set an equivalence between representations...
We are going to use the Euler's vector fields in order to show that for real quasi-homogeneous singularities with isolated critical value, the Milnor's fibration in a "thin" hollowed tube involving the zero level and the fibration in the complement...
Instead of the 'bag-of-words' representation, in the quantitative profile approach to spam filtering and email categorization, an email is represented by an m-dimensional vector of numbers, with m fixed in advance. Inspired by Sroufe et al. [Sroufe,...
We express any Courant algebroid bracket by means of a metric connection, and construct a Courant algebroid structure on any orthogonal Whitney sum $E\oplus C$ where E is a given Courant algebroid and C is a flat, pseudo- Euclidean vector bundle. T...
In differential geometry, a field of mathematics, a Courant algebroid is a vector bundle together with an inner product and a compatible bracket more
We introduce the Courant algebroid lift, a new construction that takes a Courant algebroid together with a vector bundle connection and produces, when the connection is flat in the image of the anchor, a Courant algebroid. In general, this lift produ...