arXiv research

The Atiyah-Patodi-Singer index theorem describes the bulk-edge correspondence of symmetry protected topological insulators. The mathematical setup for this theorem is, however, not directly related to the physical fermion system, as it imposes on the fermion fields a non-local and unnatural boundary condition known as …

We propose a non-perturbative formulation of the Atiyah-Patodi-Singer(APS) index in lattice gauge theory, in which the index is given by the $η$ invariant of the domain-wall Dirac operator. Our definition of the index is always an integer with a finite lattice spacing. To verify this proposal, using the eigenmode set o…

We give an Atiyah-Patodi-Singer index theory construction of the bundle of fermionic Fock spaces parametrized by vector potentials in odd space dimensions and prove that this leads in a simple manner to the known Schwinger terms (Faddeev-Mickelsson cocycle) for the gauge group action. We relate the APS construction to …

We investigate index theory in the context of Dirac operators coupled to superconnections. In particular, we prove a local index theorem for such operators, and for families of such operators. We investigate eta-invariants and prove an APS-theorem, and construct a geometric determinant line bundle for families of such …

We provide an interpretation of the APS index theorem of Piazza-Schick and Zeidler in terms of coarse homotopy theory. On the one hand we propose a motivic version of the boundary value problem, the index theorem, and the associated secondary invariants. On the other hand, we discuss in detail how the abstract version …

Study perturbs APS boundary conditions for Lorentzian Dirac operators.

Study Dirac operators on finite warped cylinders with gauge fields.

New perspective on APS indices preserves orientations and gradings through bordisms.

We discuss the behaviour of the signature index class of closed foliated bundles under the operation of cutting and pasting. Along the way we establish several index theoretic results: we define Atiyah-Patodi-Singer (APS) index classes for Dirac-type operators on foliated bundles with boundary; we prove a relative inde…

The class of metrizable spaces $M$ with the following approximation property is introduced and investigated: $M\in AP(n,0)$ if for every $\e>0$ and a map $g\colon\I^n\to M$ there exists a 0-dimensional map $g'\colon\I^n\to M$ which is $\e$-homotopic to $g$. It is shown that this class has very nice properties. For exam…

New examples show positive scalar curvature metrics on manifolds with boundary that cannot be extended.

We compute the index of a Callias-type operator with APS boundary condition on a manifold with compact boundary in terms of combination of indexes of induced operators on a compact hypersurface. Our result generalizes the classical Callias-type index theorem to manifolds with compact boundary.

We study the index of the APS boundary value problem for a strongly Callias-type operator $D$ on a complete even dimensional Riemannian manifold $M$ (the odd dimensional case was considered in our previous paper arXiv:1706.06737). We use this index to define the relative $η$-invariant $η(A_1,A_0)$ of two strongly Calli…

Study improves scalability of cell-free massive MIMO networks by optimizing UE-AP association.

Introduces robust and decomposable AP for image retrieval.

Study well-poses Dirac operator problem with APS boundary conditions.

Index theorems for the Dirac operator allow one to study spinors on manifolds with boundary and torsion. We analyse the modifications of the boundary Chern-Simons correction and APS eta invariant in the presence of torsion. The bulk contribution must also be modified and is computed using a supersymmetric quantum mecha…

Study reflection symmetry and APS boundary conditions on a warped cylinder.

Study optimal portfolio selection using average and current profitability of risky assets.

An absolute parallelism (AP-) space having Finslerian properties is called FAP-space. This FAP-structure is more wider than both conventional AP and Finsler structures. In the present work, more geometric objects as curvature and torsion tensors are derived in the context of this structure. Also second order tensors, u…

Detects project management anti-patterns using code and issue data.

New method automates asymmetric choice for better skill transfer in reinforcement learning.

With the recent development in mobile computing devices and as the ubiquitous deployment of access points(APs) of Wireless Local Area Networks(WLANs), WLAN based indoor localization systems(WILSs) are of mounting concentration and are becoming more and more prevalent for they do not require additional infrastructure. A…

Reformulates mod-two APS index using domain-wall fermion.

Study spectral flow on a warped cylinder with special boundary conditions.

New boundary conditions solve Cauchy problem for Dirac operators on spacetimes.

Discrete diffusion models improve text and image inference.

Paper proposes a graph model for optimal AP deployment in indoor optical wireless networks.

We consider a generalized APS boundary problem for a G-invariant Dirac-type operator, which is not of product type near the boundary. We establish a delocalized version (a so-called Kirillov formula) of the equivariant index theorem for this operator. We obtain more explicit formulas for different geometric Dirac-type …

New framework uses MABs for better WLAN performance.

Eigenvalue estimate for the Dirac-Witten operator is given on bounded domains (with smooth boundary) of spacelike hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS, and chiral conditions). This result is a generalisation of Friedrich's inequality for …

Assisted by neural networks, reinforcement learning agents have been able to solve increasingly complex tasks over the last years. The simulation environment in which the agents interact is an essential component in any reinforcement learning problem. The environment simulates the dynamics of the agents' world and henc…

PHBench predicts Series A funding from Product Hunt launch signals with 7.8% accuracy.

In this paper, we deal with a generalization of the geometry of parallelizable manifolds, or the absolute parallelism (AP-) geometry, in the context of generalized Lagrange spaces. All geometric objects defined in this geometry are not only functions of the positional argument $x$, but also depend on the directional ar…

In the present work, it is shown that, the application of the Bazanski approach to Lagrangians, written in AP-geometry and including the basic vector of the space, gives rise to a new class of path equations. The general equation representing this class contains four extra terms, whose vanishing reduces this equation t…

AP-Calculus offers a new framework for causal inference in Bayesian networks.

In this paper we first establish the relation between the zeta-determinant of a Dirac Laplacian with the Dirichlet boundary condition and the APS boundary condition on a cylinder. Using this result and the gluing formula of the zeta-determinant given by Burghelea, Friedlander and Kappeler with some assumptions, we prov…

Modern treatments for Type 1 diabetes (T1D) use devices known as artificial pancreata (APs), which combine an insulin pump with a continuous glucose monitor (CGM) operating in a closed-loop manner to control blood glucose levels. In practice, poor performance of APs (frequent hyper- or hypoglycemic events) is common en…

In future cell-free (or cell-less) wireless networks, a large number of devices in a geographical area will be served simultaneously in non-orthogonal multiple access scenarios by a large number of distributed access points (APs), which coordinate with a centralized processing pool. For such a centralized cell-free net…

Extends Onsager's conjecture to Besov spaces on manifolds with boundary.

Detects knots in thickened surfaces using instanton homology.

New rigidity theorems for spin fill-ins with non-negative scalar curvature.

Designing a photometric system to best fulfil a set of scientific goals is a complex task, demanding a compromise between conflicting requirements and subject to various constraints. A specific example is the determination of stellar astrophysical parameters (APs) - effective temperature, metallicity etc. - across a wi…

Paper proposes a DRL-based controller for networked AP systems that reduces communication frequency.

Let (M, π ) be a Poisson manifold. A Poisson submanifold $P \in M$ gives rise to an algebroid $AP \rightarrow P$, to which we associate certain chomology groups which control formal deformations of π around P . Assuming that these groups vanish, we prove that π is formally rigid around P , i.e. any other Poisson struct…

Recently, it has been shown that Absolute Parallelism (AP) geometry admits paths that are naturally quantized. These paths have been used to describe the motion of spinning particles in a background gravitational field. In case of a weak static gravitational field limits, the paths are applied successfully to interpret…

Formula for index in Lorentzian spacetimes.

In this article we examine the conjecture of Neumann and Reid that the only hyperbolic knots in the $3$-sphere which admit hidden symmetries are the figure-eight knot and the two dodecahedral knots. Knots whose complements cover hyperbolic reflection orbifolds admit hidden symmetries, and we verify the Neumann-Reid con…