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www.mixedbread.com/blog/toast-1

Introducing Toast 1

Meet Toast 1, Mixedbread's search agent for knowledge-intensive tasks, matching or outperforming Claude Opus 5 and GPT-5.6 Sol while being up to 10× cheaper and 12× faster.

arxiv.org/abs/1803.07160v2

Microwave Vortex Beam Launcher Design

A novel design for a vectorial vortex beam launcher in the microwave regime is devised. The beam is formed by launching a single guided transverse electric (TE) mode of a metallic circular waveguide into free-space. Excitation is achieved by the mean...

arxiv.org/abs/2602.20833v5

DRESS: A Continuous Framework for Structural Graph Refinement

We introduce DRESS, a deterministic, parameter-free framework that iteratively refines the structural similarity of edges in a graph to produce a canonical fingerprint: a real-valued edge vector, obtained by converging a non-linear dynamical system t...

github.com/dagostinelli/hypatia

dagostinelli/hypatia

A header-only, pure-C math library for 2D/3D graphics (matrix, vector, quaternion) Seeks to be close to C89/C90 compliant for portability. It's like a BLAS, but easier to use. (⭐ 100)

arxiv.org/abs/0711.3944v1

Tensor product of coherent systems

Let X be a smooth algebraic curve of genus g>=2. A stable vector bundle over X of degree d, rank n with at least k sections is called a Brill-Noether bundle of type (n,d,k). By tensoring coherent systems, we prove that most of the known Brill-Noeth...

en.wikipedia.org/wiki/Frenet%E2%80%93Serret_formulas

Frenet–Serret formulas - Wikipedia

specifically, the formulas describe the derivatives of the so-called tangent, normal, and binormal unit vectors in terms of each other. The formulas are named

arxiv.org/abs/2004.09701v1

Reconciling the X(2240) with the Y(2175)

In the present work, we reanalyzed the cross sections for $e^+ e^- \to K^+K^-$, where a new structure $X(2240)$ was reported by BES III Collaboration. By including the interference between the direct coupling and vector meson intermediate processes,...

arxiv.org/abs/1605.05256v4

A Metric for Heterotic Moduli

Heterotic vacua of string theory are realised, at large radius, by a compact threefold with vanishing first Chern class together with a choice of stable holomorphic vector bundle. These form a wide class of potentially realistic four-dimensional vacu...

arxiv.org/abs/2106.11660v3

Medium effects in supernovae constraints on light mediators

In this article, we reevaluate supernovae (SN) constraints on the diffusion time of neutrinos for a family of extensions of the Standard Model that incorporate new light scalar and vector mediators. We compute the neutrino mean free path, taking into...

arxiv.org/abs/2405.10055v1

What are kets?

According to Dirac's bra-ket notation, in an inner-product space, the inner product $\langle x\,|\,y\rangle$ of vectors $x,y$ can be viewed as an application of the bra $\langle x|$ to the ket $|y\rangle$. Here $\langle x|$ is the linear functional $...

arxiv.org/abs/2507.23755v3

Slot Attention with Re-Initialization and Self-Distillation

Unlike popular solutions based on dense feature maps, Object-Centric Learning (OCL) represents visual scenes as sub-symbolic object-level feature vectors, termed slots, which are highly versatile for tasks involving visual modalities. OCL typically a...

en.wikipedia.org/wiki/Conformal_Killing_vector_field

Conformal Killing vector field - Wikipedia

globally flat coordinates in which we have a constant metric g μ ν = η μ ν {\displaystyle g_{\mu \nu }=\eta _{\mu \nu }} where in space with signature (

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