Related papers: Transverse modes for flat inter-bunch wakes

We establish necessary and sufficient conditions for invertibility of symmetric three-by-three block matrices having a double saddle-point structure \fb{that guarantee the unique solvability of double saddle-point systems}. We consider…

Transformers are deep neural network architectures that underpin the recent successes of large language models. Unlike more classical architectures that can be viewed as point-to-point maps, a Transformer acts as a measure-to-measure map…

We look at the Equivalence Theorem as a statement about the absence of polynomial infrared divergences when $m_W \rightarrow 0$. We prove their absence in a truncated toy model and conjecture that, if they exist at all, they are due to…

We study the renormalization of non-commutative gauge theories with matter. As in the scalar field theory cases, there are logarithmic infrared divergences resulting from integrating out high momentum modes. In order to reproduce the…

Quandles can be regarded as generalizations of symmetric spaces. In the study of symmetric spaces, the notion of flatness plays an important role. In this paper, we define the notion of flat quandles, by referring to the theory of…

We consider a bouncing Universe model which explains the flatness of the primordial scalar spectrum via complex scalar field that rolls down its negative quartic potential and dominates in the Universe. We show that in this model, there…

We present two main theorems along the lines of Lyapunov's second method that guarantee asymptotic state consensus in multi-agent systems of agents in R^m with switching interconnection topologies. The two theorems complement each other in…

Arrays of transmons have proven to be a viable medium for quantum information science and quantum simulations. Despite their widespread popularity as qubit arrays, there remains yet untapped potential beyond the two-level approximation or,…

With a steady increase in the inverter technology integration to the grid, frequency response of the large inter-connection system becomes more unpredictable. This leads to a significant change in the boundaries of the coherent region,…

We develop some aspects of the homological algebra of persistence modules, in both the one-parameter and multi-parameter settings, considered as either sheaves or graded modules. The two theories are different. We consider the graded module…

We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The…

Let X be a complex surface with no nontrivial 2-forms. Then we show that Bloch's conjecture is true (i.e. the Albanese map in this case is injective) if and only if any homologically trivial idempotent in the ring of correspondences…

Conditions for the existence, uniqueness and stability of self-consistent bunch steady states are considered. For the existence and uniqueness problems, simple algebraic criteria are derived for both the action and Hamiltonian domain…

If the fundamental type-I string scale is of the order of few TeV, the problem of the gauge hierarchy is that of understanding why some dimensions transverse to our brane-world are so large. The technical aspect of this problem, as usually…

The envelope theory is a simple technique to obtain approximate, but reliable, solutions of many-body systems with identical particles. The accuracy of this method is tested here for two systems in one dimension with pairwise forces. The…

Large language models exhibit sophisticated capabilities, yet understanding how they work internally remains a central challenge. A fundamental obstacle is that training selects for behavior, not circuitry, so many weight configurations can…

Let G be a connected complex Lie group. We show that any flat principal G-bundle over any finite CW-complex pulls back to a trivial bundle over some finite covering space of the base space if and only if each real characteristic class of…

In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…

Transformers have recently revolutionized many domains in modern machine learning and one salient discovery is their remarkable in-context learning capability, where models can solve an unseen task by utilizing task-specific prompts without…

Many observables in quantum field theory can be expressed in terms of trans-series, in which one adds to the perturbative series a typically infinite sum of exponentially small corrections, due to instantons or to renormalons. Even after…