Unitary Positive-Energy Representations of Scalar Bilocal Quantum Fields

The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective gauge groups U(N) and O(N) confirms the expectations based on general results obtained in the framework of local nets in algebraic quantum field theory, but the approach using standard Lie algebra methods rather than abstract duality theory is complementary. The result indicates that one does not lose interesting models if one postulates the absence of scalar fields of dimension D-2 in models with global conformal invariance. Another remarkable outcome is the observation that, with an appropriate choice of the Hamiltonian, a Lie algebra embedded into the associative algebra of observables completely fixes the representation theory.Comment: 27 pages, v3: result improved by eliminating redundant assumptio

Entire curves avoiding given sets in C^n

Let $F\subset\Bbb C^n$ be a proper closed subset of $\Bbb C^n$ and $A\subset\Bbb C^n\setminus F$ at most countable ($n\geq 2$). We give conditions of $F$ and $A$, under which there exists a holomorphic immersion (or a proper holomorphic embedding) $\phi:\Bbb C\to\Bbb C^n$ with $A\subset\phi(\Bbb C)\subset\Bbb C^n\setminus F$.Comment: 10 page

On the Markov inequality in the L2-norm with the Gegenbauer weight

Let wλ(t):=(1−t2)λ−1/2, where λ>−12, be the Gegenbauer weight function, let ∥⋅∥wλ be the associated L2-norm, |f∥wλ={∫1−1|f(x)|2wλ(x)dx}1/2, and denote by Pn the space of algebraic polynomials of degree ≤n. We study the best constant cn(λ) in the Markov inequality in this norm ∥p′n∥wλ≤cn(λ)∥pn∥wλ,pn∈Pn, namely the constant cn(λ):=suppn∈Pn∥p′n∥wλ∥pn∥wλ. We derive explicit lower and upper bounds for the Markov constant cn(λ), which are valid for all n and λ

Diagnosing Morbus Menière through electrocochleography

Idiopathic endolymphatic hydrops is a histopathological hallmark of Menière’s disease and other volume regulation-related inner ear disorders. It manifests as a triad of symptoms: episodic vertigo, tinnitus and hearing loss. In this study we used electrocochleography in order to diagnose Menière’s disease. Electrocochleography is a method of recording the stimulus-related potentials of the cochlea and the auditory nerve. In one of the three presented cases, analysis of the electrocochleographic waveform shows endolymphatic hydrops. In diagnosing Menière’s disease, electrocochleography is a fairly consistent indicator of the presence of endolymphatic hydrops, in addition to the anamnesis and examination of patients.-------------------------------------Идиопатичният ендолимфатичен хидропс е хистопатологичният белег на Мениеровата болест и на други нарушения на обемната регулация на течностите във вътрешното ухо. Клинично се проявява с триада от симптоми, включваща епизодично вертиго, тинитус и намаление на слуха. В настоящото проучване използвахме електрокохлеография за доказване на Мениеровата болест. Това е електрофизиологичен метод, регистриращ потенциали от кохлеата и слуховия нерв в отговор на звукови стимули. Анализът на електрокохлеографската крива показва хидропс на лабиринта в един от представените три случая. Електрокохлеографията е сравнително постоянен индикатор за наличието на ендолимфатичен хидропс и допълва данните от анамнезата и физикалния преглед при доказването на Мениеровата болест

Convergence and multiplicities for the Lempert function

Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space Hol (\D,\Omega) of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii's work) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for Matemati

MVG Mechanism: Differential Privacy under Matrix-Valued Query

Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it forfeits an opportunity to exploit the structural characteristics typically associated with matrix analysis. To address this challenge, we propose a novel differential privacy mechanism called the Matrix-Variate Gaussian (MVG) mechanism, which adds a matrix-valued noise drawn from a matrix-variate Gaussian distribution, and we rigorously prove that the MVG mechanism preserves $(\epsilon,\delta)$-differential privacy. Furthermore, we introduce the concept of directional noise made possible by the design of the MVG mechanism. Directional noise allows the impact of the noise on the utility of the matrix-valued query function to be moderated. Finally, we experimentally demonstrate the performance of our mechanism using three matrix-valued queries on three privacy-sensitive datasets. We find that the MVG mechanism notably outperforms four previous state-of-the-art approaches, and provides comparable utility to the non-private baseline.Comment: Appeared in CCS'1

Jacobi Identity for Vertex Algebras in Higher Dimensions

Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus techniques and investigating the notion of polylocal fields. We derive a Jacobi identity which together with the vacuum axiom can be taken as an equivalent definition of vertex algebra.Comment: 35 pages, references adde