Miracle-dz/UniFAR-FTUs huggingface dataset:
Classical Limit of the Three-Point Function from Integrability

In the last ten years, starting with the pioneer paper by Minahan and Zarembo [1], a vast integrable structure has been unveiled in the N = 4 supersymmetric YangMills (SYM) theory [2]. There are hopes that together with the spectrum of states, the integrability can be used to compute the correlation functions of the theory. Of special interest are the correlation functions of one-trace operators in the classical limit when the length of the traces is very large. Such operators are dual to extended classical strings in the AdS5×S background, and knowing their correlation functions can shed light about the interactions at strong coupling. Recently, Escobedo, Gromov, Sever and Vieira [3, 4] developed Bethe-Ansatz techniques for computing the tree-level structure coefficient C 123 and found an expression for the latter in terms of scalar products of Bethe states for the XXX1/2 spin chain. In [4] an elegant analytic formula was derived for the classical limit of the structure coefficient of when one of the operators is protected (BPS). In this note we generalize the result of [4] to the case of three non-BPS classical operators. Our starting point will be the representation of the structure constant in terms of Slavnov-like determinants [5], proposed recently by Foda [6].
Edge connectivity and the spectral gap of combinatorial and quantum graphs

We derive a number of upper and lower bounds for the first nontrivial eigenvalue of Laplacians on combinatorial and quantum graph in terms of the edge connectivity, i.e. the minimal number of edges which need to be removed to make the graph disconnected. On combinatorial graphs, one of the bounds corresponds to a well-known inequality of Fiedler, of which we give a new variational proof. On quantum graphs, the corresponding bound generalizes a recent result of Band and Lévy. All proofs are general enough to yield corresponding estimates for the p-Laplacian and allow us to identify the minimizers. Based on the Betti number of the graph, we also derive upper and lower bounds on all eigenvalues which are ‘asymptotically correct’, i.e. agree with the Weyl asymptotics for the eigenvalues of the quantum graph. In particular, the lower bounds improve the bounds of Friedlander on any given graph for all but finitely many eigenvalues, while the upper bounds improve recent results of Ariturk. Our estimates are also used to derive bounds on the eigenvalues of the normalized Laplacian matrix that improve known bounds of spectral graph theory.
A generalization of Kátai's orthogonality criterion with applications

We study properties of arithmetic sets coming from multiplicative number theory and obtain applications in the theory of uniform distribution and ergodic theory. Our main theorem is a generalization of Katai's orthogonality criterion. Here is a special case of this theorem: Let $a\colon\mathbb{N}\to\mathbb{C}$ be a bounded sequence satisfying $$ \sum_{n\leq x} a(pn)\overline{a(qn)} = {\rm o}(x),~\text{for all distinct primes $p$ and $q$. } $$ Then for any multiplicative function $f$ and any $z\in\mathbb{C}$ the indicator function of the level set $E=\{n\in\mathbb{N}:f(n)=z\}$ satisfies $$ \sum_{n\leq x} \mathbb{1}_E(n)a(n)={\rm o}(x). $$ With the help of this theorem one can show that if $E=\{n_1 0$ with $c\notin \mathbb{N}$, $\log^r(t)$ for any $r>2$, $\log(\Gamma(t))$, $t\log(t)$, and $\frac{t}{\log t}$. The uniform distribution results, in turn, allow us to obtain new examples of ergodic sequences, i.e. sequences along which the ergodic theorem holds.
arXiv : On Matrix Factorizations, Residue Pairings and Homological Mirror Symmetry

We argue how boundary B-type Landau-Ginzburg models based on matrix factorizations can be used to compute exact superpotentials for intersecting D-brane configurations on compact Calabi-Yau spaces. In this paper, we consider the dependence of open-string, boundary changing correlators on bulk moduli. This determines, via mirror symmetry, non-trivial disk instanton corrections in the A-model. As crucial ingredient we propose a differential equation that involves matrix analogs of Saito's higher residue pairings. As example, we compute from this for the elliptic curve certain quantum products m_2 and m_3, which reproduce genuine boundary changing, open Gromov-Witten invariants.
Statistics for Analytical Chemistry

Introduction. Errors in Classical Analysis - Statistics of Repeated Measurements. Significance Tests. Quality Control and Sampling. Errors in Instrumental Analysis. Regression and Correlation. Non-parametric and Robust Methods. Experimental Design. Optimization and Pattern Recognition. Solutions to Exercises. Appendix 1: Summary of Statistical Tests. Appendix 2: Statistical Tests.
Higher-dimensional Clifford–Severi equalities

Let [Formula: see text] be a smooth complex projective variety, [Formula: see text] a morphism to an abelian variety such that [Formula: see text] injects into [Formula: see text] and let [Formula: see text] be a line bundle on [Formula: see text]; denote by [Formula: see text] the minimum of [Formula: see text] for [Formula: see text]. The so-called Clifford–Severi inequalities have been proven in [M. A. Barja, Generalized Clifford–Severi inequality and the volume of irregular varieties, Duke Math. J. 164(3) (2015) 541–568; M. A. Barja, R. Pardini and L. Stoppino, Linear systems on irregular varieties, J. Inst. Math. Jussieu (2019) 1–39; doi:10.1017/S1474748019000069]; in particular, for any [Formula: see text] there is a lower bound for the volume given by: [Formula: see text] and, if [Formula: see text] is pseudoeffective, [Formula: see text] In this paper, we characterize varieties and line bundles for which the above Clifford–Severi inequalities are equalities.
A diffeomorphism-invariant metric on the space of vector-valued one-forms

In this article we introduce a diffeomorphism-invariant metric on the space of vector valued one-forms. The particular choice of metric is motivated by potential future applications in the field of functional data and shape analysis and by connections to the Ebin-metric on the space of all Riemannian metrics. In the present work we calculate the geodesic equations and obtain an explicit formula for the solutions to the corresponding initial value problem. Using this we show that it is a geodesically and metrically incomplete space and study the existence of totally geodesic subspaces. Furthermore, we calculate the sectional curvature and observe that, depending on the dimension of the base manifold and the target space, it either has a definite sign or admits both signs.
Points on nodal lines with given direction

We study of the directional distribution function of nodal lines for eigenfunctions of the Laplacian on a planar domain. This quantity counts the number of points where the normal to the nodal line points in a given direction. We give upper bounds for the flat torus, and compute the expected number for arithmetic random waves.
Le groupe de Chow d'une surface rationnelle sur un corps local

We compute the Chow group of 0-cycles on a rational surface defined over a finite extension K of the field $\mathbb{Q}_p$ of p-adic numbers (p a prime) when it is split by an unramified extension of K. We use intersection theory to define a specialisation map so we need to assume that the surface admits a regular proper integral model. A family of examples is worked out to illustrate the method.
Dynamical Systems induced by Canonical Divergence in dually flat manifolds

The principles of classical mechanics have shown that the inertial quality of mass is characterized by the kinetic energy. This, in turn, establishes the connection between geometry and mechanics. We aim to exploit such a fundamental principle for information geometry entering the realm of mechanics. According to the modification of curve energy stated by Amari and Nagaoka for a smooth manifold $\mathrm{M}$ endowed with a dual structure $(\mathrm{g},\nabla,\nabla^*)$, we consider $\nabla$ and $\nabla^*$ kinetic energies. Then, we prove that a recently introduced canonical divergence and its dual function coincide with Hamilton principal functions associated with suitable Lagrangian functions when $(\mathrm{M},\mathrm{g},\nabla,\nabla^*)$ is dually flat. Corresponding dynamical systems are studied and the tangent dynamics is outlined in terms of the Riemannian gradient of the canonical divergence. Solutions of such dynamics are proved to be $\nabla$ and $\nabla^*$ geodesics connecting any two points sufficiently close to each other. Application to the standard Gaussian model is also investigated.
Indian ocean dipole modulates the number of extreme rainfall events over India in a warming environment

This study shows that high resolution rainfall data indicate an increase in number of extreme rainfall events over India in the last few decades. Unravelling the mechanism behind this increasing number of extreme rainfall events in central India is important as these intense rainfall events cause floods and related damage to the life and property of more than 400 million people living in this region. The natural disaster risk hotspots analysis projected the central Indian region as the most vulnerable region for floods in the Indian subcontinent. Here, we present first evidence that the extreme rainfall events in central India in recent decades are strongly modulated by cool sea surface temperature anomalies in the south-eastern equatorial Indian Ocean. The ongoing warming trend of the Indian Ocean coupled with the increase in the number of Indian Ocean Dipole years in recent decades suggests more frequent extreme rainfall events and related hazards in central India in forthcoming years.
On the effects of a weak magnetic field on turbulent transport

We discuss the effects of a weak large-scale magnetic field on turbulent transport. We show by means of a series of two-dimensional numerical experiments that turbulent diffusion can be effectively suppressed by a (large scale) magnetic field whose energy is small compared to equipartition. The suppression mechanism is associated with a subtle modification of the Lagrangian energy spectrum, and it does not require any substantial reduction of the turbulent amplitude. We exploit the relation between diffusion and random walking to emphasize that the effect of a large-scale magnetic field is to induce a long-term memory in the field of turbulence. The implications of the general case of three-dimensional transport are briefly discussed.
On the equivariance properties of self-adjoint matrices

We investigate self-adjoint matrices with respect to their equivariance properties. We show in particular that a matrix is self-adjoint if and only if it is equivariant with respect to the action of a group which is isomorphic to . If the self-adjoint matrix possesses multiple eigenvalues – this may, for instance, be induced by symmetry properties of an underlying dynamical system – then A is even equivariant with respect to the action of a group where are the multiplicities of the eigenvalues of A. We discuss implications of this result for equivariant bifurcation problems, and we briefly address further applications for the Procrustes problem, graph symmetries and Taylor expansions.
The Markov-quantile process attached to a family of marginals

Let µ = (µt)t∈R be any 1-parameter family of probability measures on R. Its quantile process (Gt)t∈R : ]0, 1[ → RR, given by Gt(α) = inf{x ∈ R : µt(]−∞, x]) > α}, is not Markov in general. We modify it to build the Markov process we call “Markov-quantile”. We ﬁrst describe the discrete analogue: if (µn)n∈Z is a family of probability measures on R, a Markov process Y = (Yn)n∈Z such that Law(Yn) = µn is given by the data of its couplings from n to n + 1, i.e. Law((Yn, Yn+1)), and the process Y is the inhomogeneous Markov chain having those couplings as transitions. Therefore, there is a canonical Markov process with marginals µn and as similar as possible to the quantile process: the chain whose transitions are the quantile couplings. We show that an analogous process exists for a continuous parameter t: there is a unique Markov process X with the measures µt as marginals, and being a limit for the ﬁnite dimensional topology of quantile processes where the past is made independent of the future at ﬁnitely many times (many non-Markovian limits exist in general). The striking fact is that the construction requires no regularity for the family µ. We rely on order arguments, which seems to be completely new for the purpose. We also prove new results the Markov-quantile process yields in two contemporary frameworks: – In case µ is increasing for the stochastic order, X has increasing trajectories. This is an analogue of a result of Kellerer dealing with the convex order, peacocks and martingales. Modiﬁying Kellerer’s proof, we also prove simultaneously his result and ours in this case. – If µ is absolutely continuous in Wasserstein space P2(R) then X is solution of a Benamou–Brenier transport problem with marginals µt. It provides a Markov probabilistic representation of the continuity equation, unique in a certain sense.
Subgraphs in preferential attachment models

Abstract We consider subgraph counts in general preferential attachment models with power-law degree exponent $\tau > 2$ . For all subgraphs H, we find the scaling of the expected number of subgraphs as a power of the number of vertices. We prove our results on the expected number of subgraphs by defining an optimization problem that finds the optimal subgraph structure in terms of the indices of the vertices that together span it and by using the representation of the preferential attachment model as a Pólya urn model.
Branes and categorifying integrable lattice models

We elucidate how integrable lattice models described by Costello's 4d Chern-Simons theory can be realized via a stack of D4-branes ending on an NS5-brane in type IIA string theory, with D0-branes on the D4-brane worldvolume sourcing a meromorphic RR 1-form, and fundamental strings forming the lattice. This provides us with a nonperturbative integration cycle for the 4d Chern-Simons theory, and by applying T- and S-duality, we show how the R-matrix, the Yang-Baxter equation and the Yangian can be categorified, that is, obtained via the Hilbert space of a 6d gauge theory.
Theory of optical scintillation: Gaussian-beam wave model

Abstract A scintillation model previously developed by the authors is extended in this paper to the case of a propagating Gaussian-beam wave. As in the previous model, we account for the loss of spatial coherence as the optical wave propagates through atmospheric turbulence by eliminating effects of certain turbulent scale sizes that exist between the scale size of the spatial coherence radius of the beam and that of the scattering disc. These mid-range scale-size effects are eliminated through the formal introduction of spatial frequency filters that continually adjust spatial cut-off frequencies as the optical wave propagates. Unlike the previous model, in this paper we include the effect of a finite outer scale in addition to the inner scale. With a finite outer scale, the scintillation index can be substantially lower in strong turbulence than that predicted by a model with an infinite outer scale. This particular behaviour of scintillation in strong turbulence, mostly associated with horizontal paths near the ground, cannot be explained on the basis of previous expressions deduced from the asymptotic theory. Comparisons of the scintillation models with published experimental and simulation data through weak and strong irradiance fluctuations show excellent fits.
Chow-Witt rings of split quadrics

We compute the Chow-Witt rings of split quadrics over a field of characteristic not two. We even determine the full bigraded I-cohomology and Milnor-Witt cohomology rings, including twists by line bundles. The results on I-cohomology corroborate the general philosophy that I-cohomology is an algebro-geometric version of singular cohomology of real varieties: our explicit calculations confirm that the I-cohomology ring of a split quadric over the reals is isomorphic to the singular cohomology ring of the space of its real points.
Modeling financial assets without semimartingales

This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes. The non-arbitrage property is not excluded if the class $\cal{A}$ of admissible strategies is restricted. The classical notion of martingale is replaced with the notion of $\cal{A}$-martingale. A calculus related to $\cal{A}$ -martingales with some examples is developed. Some applications to the maximization of the utility of an insider are expanded.
Cross-Tropopause Mass Exchange and Potential Vorticity Budget in a Simulated Tropopause Folding

Abstract To study stratosphere–troposphere exchange, an approach based on the nonconservation of potential vorticity (PV) is developed; this approach arises naturally if one defines the tropopause in terms of PV. The evolution of a tropopause fold simulated by a mesoscale model is studied, as well as the evolution of PV at the tropopause level. The PV framework also permits the identification of the physical processes responsible for the cross-tropopause exchange as either diffusive or diabatic. In this model simulation, the diabatic processes are found to be the most important in the exchange. In particular, it is found that the negative heating gradient in the region of the warm sector of the surface cyclone is responsible for most of the diabatic exchange across the tropopause. The mass exchange during the tropopause folding event is estimated to be around 4.9 × 1014 kg in four days over the domain considered (1600 × 2000 km). This number is shown to correspond to the net difference between exchange fr.
Fast microchannel plate detector with an impedance matched anode in suspended substrate technology

Fast particle detectors with subnanosecond pulse widths are key elements in modern time-of-flight mass spectrometers. Typically, an impedance matched transmission line from the extended anode to the coaxial cable is necessary to obtain fast pulses. We present an approach using a planar geometry for the transmission line. Thereby, the impedance match is realized with a transition from a 50 Ω suspended substrate microstrip line to a coaxial 50 Ω line. A prototype with an active area of 1.8 cm diameter including a strategy to reduce peak ringing was built and tested. The mean pulse width measured with a 1 GHz analog oscilloscope was 520 ps (full width at half maximum) with a rise time of 380 ps. The robust, compact, and low-weight design of the detector is well suited for an application in space, where weight, space, and power consumption are very limited resources.
Università di Milano – Bicocca Quaderni di Matematica Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian

We consider Hamilton Jacobi Bellman equations in an inifinite dimensional Hilbert space, with quadratic (respectively superquadratic) hamiltonian and with continuous (respectively lipschitz continuous) final conditions. This allows to study stochastic optimal control problems for suitable controlled Ornstein Uhlenbeck process with unbounded control processes.
Superbroadband high-power superluminescent diode emitting at 920 nm

The physical parameters of superluminescent diodes (SLDs) based on a single-layer quantum-well heterostructure with the (InGa)As active layer and a graded-index waveguide are studied. The power at the output of a single-mode fibre aligned with respect to the diode was 1 — 10 mW in the regime of spatially homogeneous injection depending on the length of the SLD active channel. The width of the emission spectrum was 100 — 110 nm, corresponding to the coherence length 7.6 — 8.8 μm.
Joint-range convexity for a pair of inhomogeneous quadratic functions and applications to QP

We establish various extensions of the convexity Dines theorem for a (joint-range) pair of inhomogeneous quadratic functions. If convexity fails we describe those rays for which the sum of the joint-range and the ray is convex. These results are suitable for dealing nonconvex inhomogeneous quadratic optimization problems under one quadratic equality constraint. As applications of our main results, different sufficient conditions for the validity of S-lemma (a nonstrict version of Finsler's theorem) for inhomogenoeus quadratic functions, is presented. In addition, a new characterization of strong duality under Slater-type condition is established.
Applications of Magnetic PsiDO Techniques to Space-adiabatic Perturbation Theory

In this review, we show how advances in the theory of magnetic pseudodifferential operators (magnetic ΨDO) can be put to good use in space-adiabatic perturbation theory (SAPT). As a particular example, we extend results of [24] to a more general class of magnetic fields: we consider a single particle moving in a periodic potential which is subjectd to a weak and slowly-varying electromagnetic field. In addition to the semiclassical parameter ε ≪ 1 which quantifies the separation of spatial scales, we explore the influence of an additional parameter λ that allows us to selectively switch off the magnetic field. We find that even in the case of magnetic fields with components in C∞ b (R), e. g. for constant magnetic fields, the results of Panati, Spohn and Teufel hold, i. e. to each isolated family of Bloch bands, there exists an associated almost invariant subspace of L (R) and an effective hamiltonian which generates the dynamics within this almost invariant subspace. In case of an isolated non-degenerate Bloch band, the full quantum dynamics can be approximated by the hamiltonian flow associated to the semiclassical equations of motion found in [24].
Radial electric fields and global electrostatic microinstabilities in tokamaks and stellarators

The effects of applied radial electric fields on the stability of ion temperature gradient (ITG) modes and trapped particle modes are investigated with a full radius gyrokinetic formulation in both axisymmetric and helically symmetric configurations. The validity of a simplified stabilization criterion often applied to experimental analysis (the shearing rate larger than the linear growth rate) is examined for various profiles of E×B flows using an expression for the shearing rate derived for arbitrary quasisymmetric geometries [T. S. Hahm, Phys. Plasmas 4, 4074 (1997)]. The results show that the criterion holds for profiles with finite shearing rate and for toroidal, helical, and slab-like ITG modes. However, it is not always applicable for trapped particle instabilities: a case is shown for which E×B flows are destabilizing. For profiles with zero shearing rate, another stabilizing mechanism is found for toroidal and helical ITG modes but not for slab-like modes.
Entanglement-annihilating and entanglement-breaking channels

We introduce and investigate a family of entanglement-annihilating channels. These channels are capable of destroying any quantum entanglement within the system they act on. We show that they are not necessarily entanglement breaking. In order to achieve this result we analyze the subset of locally entanglement-annihilating channels. In this case, the same local noise applied on each subsystem individually is less entanglement annihilating (with respect to multi-partite entanglement) as the number of subsystems is increasing. Therefore, the bipartite case provides restrictions on the set of local entanglement-annihilating channels for the multipartite case. The introduced concepts are illustrated on the family of single-qubit depolarizing channels.