Boundary relations and generalized resolvents of symmetric operators

The Kre\u{\i}n-Naimark formula provides a parametrization of all selfadjoint exit space extensions of a, not necessarily densely defined, symmetric operator, in terms of maximal dissipative (in \dC_+) holomorphic linear relations on the parameter space (the so-called Nevanlinna families). The new notion of a boundary relation makes it possible to interpret these parameter families as Weyl families of boundary relations and to establish a simple coupling method to construct the generalized resolvents from the given parameter family. The general version of the coupling method is introduced and the role of boundary relations and their Weyl families for the Kre\u{\i}n-Naimark formula is investigated and explained.Comment: 47 page

Boundary triplets for skew-symmetric operators and the generation of strongly continuous semigroups

We give a self-contained and streamlined exposition of a generation theorem for C0-semigroups based on the method of boundary triplets. We apply this theorem to port-Hamiltonian systems where we discuss recent results appearing in stability and control theory. We give detailed proofs and require only a basic knowledge of operator and semigroup theory.Comment: 19 page

A functional model, eigenvalues, and finite singular critical points for indefinite Sturm-Liouville operators

Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach to the problem is given via a functional model for indefinite Sturm-Liouville operators. Algebraic multiplicities of eigenvalues are obtained. Also, operators with finite singular critical points are considered.Comment: 38 pages, Proposition 2.2 and its proof corrected, Remarks 2.5, 3.4, and 3.12 extended, details added in subsections 2.3 and 4.2, section 6 rearranged, typos corrected, references adde

Schrödinger operators with δ and δ′-potentials supported on hypersurfaces

Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity results on the functions in their domains are obtained, and analogues of the Birman–Schwinger principle and a variant of Krein’s formula are shown. Furthermore, Schatten–von Neumann type estimates for the differences of the powers of the resolvents of the Schrödinger operators with δ and δ′-potentials, and the Schrödinger operator without a singular interaction are proved. An immediate consequence of these estimates is the existence and completeness of the wave operators of the corresponding scattering systems, as well as the unitary equivalence of the absolutely continuous parts of the singularly perturbed and unperturbed Schrödinger operators. In the proofs of our main theorems we make use of abstract methods from extension theory of symmetric operators, some algebraic considerations and results on elliptic regularity

Deep learning for inferring cause of data anomalies

Daily operation of a large-scale experiment is a resource consuming task, particularly from perspectives of routine data quality monitoring. Typically, data comes from different sub-detectors and the global quality of data depends on the combinatorial performance of each of them. In this paper, the problem of identifying channels in which anomalies occurred is considered. We introduce a generic deep learning model and prove that, under reasonable assumptions, the model learns to identify 'channels' which are affected by an anomaly. Such model could be used for data quality manager cross-check and assistance and identifying good channels in anomalous data samples. The main novelty of the method is that the model does not require ground truth labels for each channel, only global flag is used. This effectively distinguishes the model from classical classification methods. Being applied to CMS data collected in the year 2010, this approach proves its ability to decompose anomaly by separate channels.Comment: Presented at ACAT 2017 conference, Seattle, US

Spin-dependent recombination mechanisms for quintet bi-excitons generated through singlet fission

We investigate the physical mechanisms for spin-dependent recombination of a strongly bound pair of triplet excitons generated by singlet fission and forming a spin quintet (total spin of two) bi-exciton. For triplet excitons the spin-dependent recombination pathways can involve intersystem crossing or triplet-triplet annihilation back to the singlet ground state. However the modeling of spin-dependent recombination for quintets is still an open question. Here we introduce two theoretical models and compare their predictions with the broadband optically detected magnetic resonance spectrum of a long lived quintet bi-exciton with known molecular structure. This spectrum measures the change in the fluorescence signal induced by microwave excitation of each of the ten possible spin transitions within the quintet manifold as function of the magnetic field. While most of the experimental features can be reproduced for both models, the behavior of some of the transitions is only consistent with the quintet spin-recombination model inspired by triplet intersystem crossing which can reproduce accurately the experimental two-dimensional spectrum with a small number of kinetic parameters. Thus quantitative analysis of the broadband optically detected magnetic resonance signal enables quantitative understanding of the dominant spin-recombination processes and estimation of the out-of equilibrium spin populations.Comment: optimization code available at https://github.com/yneter/ampodm

Orthogonal polynomials of discrete variable and Lie algebras of complex size matrices

We give a uniform interpretation of the classical continuous Chebyshev's and Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie algebra gl(N), where N is any complex number. One can similarly interpret Chebyshev's and Hahn's q-polynomials and introduce orthogonal polynomials corresponding to Lie superlagebras. We also describe the real forms of gl(N), quasi-finite modules over gl(N), and conditions for unitarity of the quasi-finite modules. Analogs of tensors over gl(N) are also introduced.Comment: 25 pages, LaTe

Prospective serum metabolomic profiling of lethal prostate cancer

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152026/1/ijc32218.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152026/2/ijc32218_am.pd

Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functions

© 2020 The Authors. Mathematische Nachrichten published by Wiley‐VCH Verlag GmbH & Co. KGaA. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.fi=vertaisarvioitu|en=peerReviewed

The Unitarity Triangle Analysis within and beyond the Standard Model

International audienceWe present the status of the Unitarity Triangle Analysis (UTA) performed by the UTfit Collaboration, with experimental and theoretical inputs updated for the last summer conferences. Several analyses are presented, corresponding to different assumptions for the theoretical model, that is either the Standard Model, or Minimal Flavour Violation orc ompletely generic NewPhysics