Miracle-dz/UniFAR-FTUs huggingface dataset:
Optical Manipulation of Light Scattering in Cold Atomic Rubidium

A brief perspective on light scattering in dense and cold atomic rubidium is presented. We particularly focus on the influence of auxiliary applied fields on the system response to a weak and nearly resonant probe field. Auxiliary fields can strongly disturb light propagation; in addition to the steady state case, dynamically interesting effects appear clearly in both the time domain, and in the optical polarization dependence of the processes. Following a general introduction, two examples of features found in such studies are presented. These include nonlinear optical effects in (a) comparative studies of forward- and fluorescence-configuration scattering under combined excitation of a control and probe field, and (b) manipulation of the spatial structure of the optical response due to a light shifting strong applied field.
Notes on well-distributed minimal sub-BIBDs for $\lambda=1$

In these notes we investigate BIBDs with $\lambda=1$ that present subdesigns evenly covering both blocks and vertices: we determine some of their basic properties, consequence of already existing results in the literature, with regards to their size and the number of intersections of pairs and triples of subdesigns of a specific kind. We also describe the link between these particular BIBDs and the graph isomorphism problem, based on Babai's paper, and point out the characteristics of these designs that would lead to improvements of the algorithm for the GIP.
A condition for long-range order in discrete spin systems with application to the antiferromagnetic Potts model

We give a general condition for a discrete spin system with nearest-neighbor interactions on the $\mathbb{Z}^d$ lattice to exhibit long-range order. The condition is applicable to systems with residual entropy in which the long-range order is entropically driven. As a main example we consider the antiferromagnetic $q$-state Potts model and rigorously prove the existence of a broken sub-lattice symmetry phase at low temperature and high dimension -- a new result for $q\ge 4$. As further examples, we prove the existence of an ordered phase in a clock model with hard constraints and extend the known regime of the demixed phase in the lattice Widom-Rowlinson model.
Kozlov-Maz'ya iteration as a form of Landweber iteration

We consider the alternating method of Kozlov and Maz'ya for solving the Cauchy problem for elliptic boundary-value problems. Considering the case of the Laplacian, we show that this method can be recast as a form of Landweber iteration. In addition to conceptual advantages, this observation leads to some practical improvements. We show how to accelerate Kozlov-Maz'ya iteration using the conjugate gradient algorithm, and we show how to modify the method to obtain a more practical stopping criterion.
Quantum $q$-Langlands Correspondence

We formulate a two-parameter generalization of the geometric Langlands correspondence, which we prove for all simply-laced Lie algebras. It identifies the q-conformal blocks of the quantum affine algebra and the deformed W-algebra associated to two Langlands dual Lie algebras. Our proof relies on recent results in quantum K-theory of the Nakajima quiver varieties. The physical origin of the correspondence is the 6d little string theory. The quantum Langlands correspondence emerges in the limit in which the 6d string theory becomes the 6d conformal field theory with (2,0) supersymmetry.
Multidimensional operator multipliers

W eintroducem ultidim ensionalSchurm ultipliersand characterise them generalising wellknown resultsby G rothendieck and Peller.W e de neam ultidim ensionalversion ofthetwodim ensionaloperatorm ultipliersstudied recentlybyK issin and Shulm an.Them ultidim ensional operator m ultipliers are de ned as elem ents of the m inim altensor productofseveralC*-algebras satisfying certain boundednessconditions. In the case ofcom m utative C*-algebras,the m ultidim ensional operatorm ultipliersreducetocontinuousm ultidim ensionalSchurm ultipliers. W e show that the m ultipliers with respect to som e given representationsofthecorresponding C*-algebrasdo notchangeifthe representationsarereplaced by approxim ately equivalentones.W eestablish a non-com m utative and m ultidim ensionalversion ofthe characterisations by G rothendieck and Peller which showsthatuniversal operatorm ultiplierscan beobtained ascertain weak lim itsofelem ents ofthe algebraic tensorproductofthe corresponding C*-algebras.
The structures of state space concerning Quantum Dynamical Semigroups

Each semigroup describing the time evolution of an open quantum system on a finite dimensional Hilbert space is related to a special structure of this space. It is shown how the space can be decomposed into subspaces: One is related to decay, orthogonal subspaces support the stationary states. Specialities where the complete positivity of evolutions is actually needed for analysis, mainly for evolution of coherence, are highlighted. Decompositions are done the same way for evolutions in discrete as in continuous time, but evolutions may show differences, only for discrete semigroups there may appear cases of sudden decay and of perpetual oscillation. Concluding the analysis we identify the relation of the state space structure to the processes of Decay, Decoherence, Dissipation and Dephasing.
Four-qubit pure states as fermionic states

The embedding of the $n$-qubit space into the $n$-fermion space with $2n$ modes is a widely used method in studying various aspects of these systems. This simple mapping raises a crucial question: does the embedding preserve the entanglement structure? It is known that the answer is affirmative for $n=2$ and $n=3$. That is, under either local unitary (LU) operations or with respect to stochastic local operations and classical communication (SLOCC), there is a one-to-one correspondence between the 2- (or 3)-qubit orbits and the 2- (or 3)-fermion orbits with 4 (or 6) modes. However these results do not generalize as the mapping from the $n$-qubit orbits to the $n$-fermion orbits with $2n$ modes is no longer surjective for $n>3$. Here we consider the case of $n=4$. We show that surprisingly, the orbit mapping from qubits to fermions remains injective under SLOCC, and a similar result holds under LU for generic orbits. As a byproduct, we obtain a complete answer to the problem of SLOCC equivalence of pure 4-qubit states.
Gromov-Hausdorff distances for dynamical systems

We study equivariant Gromov-Hausdorff distances for general continuous actions which are not necessarily isometric as Fukaya introduced. We prove that if an action is expansive and has pseudo-orbit tracing property then it is stable under our adapted equivariant Gromov-Hausdorff topology. Finally, using Lott and Villani's ideas of optimal transport in studying curvature-dimension conditions, we investigate equivariant Gromov-Hausdorff convergence for actions of locally compact amenable groups on Wasserstein spaces.
Molecular accretion in the core of the galaxy cluster 2A 0335+096

We present adaptive optics-assisted K-band integral field spectroscopy of the central cluster galaxy in 2A 0335+096 (z= 0.0349). The H2 v=1–0 S(1) emission is concentrated in two peaks within 600 pc of the nucleus and fainter but kinematically active emission extends towards the nucleus. The H2 is in a rotating structure which aligns with, and appears to have been accreted from, a stream of Hα emission extending over 14 kpc towards a companion galaxy. The projected rotation axis aligns with the 5 GHz radio lobes. This H2 traces the known 1.2 × 109 M⊙ CO-emitting reservoir; limits on the Brγ emission confirm that the H2 emission is not excited by star formation, which occurs at a rate of less than 1 M⊙ yr−1 in this gas. If its accretion on to the black hole can be regulated whilst star formation remains suppressed, the reservoir could last for at least 1 Gyr; the simultaneous accretion of just ∼5 per cent of the gas could drive a series of active galactic nucleus (AGN) outbursts which offset X-ray cooling in the cluster core for the full ∼1 Gyr. Alternatively, if the regulation is ineffective and the bulk of the H2 accretes within a few orbital periods (25–100 Myr), the resulting 1062 erg outburst would be among the most powerful cluster AGN outbursts known. In either case, these observations further support cold feedback scenarios for AGN heating.
Interacting double coset magnons

We consider the anomalous dimensions of restricted Schur polynomials constructed using $n\ensuremath{\sim}O(N)$ complex adjoint scalars $Z$ and $m$ complex adjoint scalars $Y$. We fix $m\ensuremath{\ll}n$ so that our operators are almost half Bogomol'nyi-Prasad-Sommerfield. At leading order in $\frac{m}{n}$ this system corresponds to a dilute gas of $m$ free magnons. Adding the first correction of order $\frac{m}{n}$ to the anomalous dimension, which arises at two loops, we find nonzero magnon interactions. The form of this new operator mixing is studied in detail for a system of two giant gravitons with four strings attached.
Higher Operads, Higher Categories

Part I. Background: 1. Classical categorical structures 2. Classical operads and multicategories 3. Notions of monoidal category Part II. Operads. 4. Generalized operads and multicategories: basics 5. Example: fc-multicategories 6. Generalized operads and multicategories: further theory 7. Opetopes Part III. n-categories: 8. Globular operads 9. A definition of weak n-category 10. Other definitions of weak n-category Appendices: A. Symmetric structures B. Coherence for monoidal categories C. Special Cartesian monads D. Free multicategories E. Definitions of trees F. Free strict n-categories G. Initial operad-with-contraction.
Effects of a lower limb rehabilitation robot with various training modes in patients with stroke: A randomized controlled trial

Background: The effect of robot-assisted gait training has been demonstrated to improve gait recovery in patients with stroke. The aim of this study was to determine effects of robot-assisted gait training with various training modes in patients post stroke. Methods: Forty-seven patients post stroke were randomly assigned to one of 4 groups: Healbot T with pelvic off mode (pelvic off group; n = 11); Healbot T with pelvic control mode (pelvic on group; n = 12); Healbot T with constraint-induced movement therapy (CIMT) mode (CIMT group; n = 10); and conventional physiotherapy (control group; n = 10). All patients received a 30-minute session 10 times for 4 weeks. The primary outcomes were the 10-meter walk test (10MWT) and Berg Balance Scale (BBS). The secondary outcomes were functional ambulation category, timed up and go (TUG), and motricity index of the lower extremities (MI-Lower). Results: The pelvic off group showed significant improvements in BBS, TUG, and MI-Lower (P < .05). The pelvic on and CIMT groups showed significant improvement in 10MWT, BBS, TUG, and MI-Lower (P < .05). Compared with control group, the pelvic on group showed greater improvement in the TUG and BBS scores; the CIMT group showed greater improvement in 10MWT and MI-Lower (P < .05). Conclusion: This study suggested that Healbot T-assisted gait training benefited patients with stroke. The Healbot T with pelvic motion and CIMT modes were more helpful in improving balance and walking ability and lower limb strength, respectively, compared with conventional physiotherapy.
On the limited amplitude resolution of multipixel Geiger-mode APDs

The limited number of active pixels in a Geiger-mode Avalanche Photodiode (G-APD) results not only in a non-linearity but also in an additional fluctuation of its response. Both these effects are taken into account to calculate the amplitude resolution of an ideal G-APD, which is shown to be finite. As one of the consequences, the energy resolution of a scintillation detector based on a G-APD is shown to be limited to some minimum value defined by the number of pixels in the G-APD. PACS numbers: 85.60. Gz
Diquark representations for single heavy baryons with light staggered quarks

In the staggered fermion formulation of lattice QCD, we construct and classify the diquark operators to be embedded in the singly heavy baryons, qqQ. Along the same manner as in the staggered meson classifications given in [M.F. L. Golterman, Nucl. Phys. B273, 663 (1986). ], we establish the group theoretical connections between continuum and lattice staggered diquark representations.
Rayleigh-Taylor instability for the two-phase Navier-Stokes equations with surface tension in cylindrical domains

This article is concerned with the dynamic behaviour of two immiscible and incompressible fluids in a cylindrical domain, which are separated by a sharp interface. In case that the heavy fluid is situated on top of the light fluid, one expects that the fluid on top sags down into the lower phase. This effect is known as the Rayleigh-Taylor-Instability. We present a rather complete analysis of the corresponding free boundary problem which involves a contact angle. Our main result implies the existence of a critical surface tension with the following property. In case that the surface tension of the interface separating the two fluids is smaller than the critical surface tension, one has Rayleigh-Taylor-Instability. On the contrary, if the interface has a greater surface tension than the critical value, the instability effect does not occur and one has exponential stability of a flat interface. The last part of this article is concerned with the bifurcation of nontrivial equilibria in multiple eigenvalues. The invariance of the corresponding bifurcation equation with respect to rotations and reflections yields the existence of bifurcating subcritical equilibria. Finally it is proven that the bifurcating equilibria are unstable.
Deformations of elliptic Calabi-Yau manifolds

Abstract We investigate deformations and characterizations of elliptic Calabi-Yau varieties, building on earlier works of Wilson and Oguiso. We show that if the second cohomology of the structure sheaf vanishes, then every deformation is again elliptic. More generally, all non-elliptic deformations derive from abelian varieties or K3 surfaces. We also give a numerical characterization of elliptic Calabi-Yau varieties under some positivity assumptions on the second Todd class. These results lead to a series of conjectures on fibered Calabi-Yau varieties. To Robert Lazarsfeld on the occasion of his sixtieth birthday The aim of this paper is to answer some questions about Calabi-Yau manifolds that were raised during the workshop String Theory for Mathematicians , which was held at the Simons Center for Geometry and Physics. F -theory posits that the “hidden dimensions” constitute a Calabi-Yau 4-fold X that has an elliptic structure with a section. That is, there are morphisms g : X → B whose general fibers are elliptic curves and σ: B → X such that g ∘ σ = 1 B (see [Vaf96, Don98]). In his lecture, Donagi asked the following: Question 1 Is every small deformation of an elliptic Calabi-Yau manifold also an elliptic Calabi-Yau manifold? Question 2 Is there a good numerical characterization of elliptic Calabi-Yau manifolds? Clearly, an answer to Question 2 should give a solution of Question 1. The answers to these problems are quite sensitive to which variant of the definition of Calabi-Yau manifolds one uses. For instance, a general deformation of the product of an Abelian variety and of an elliptic curve has no elliptic fiber space structure and every elliptic K3 surface has non-elliptic deformations. We prove in Section 5 that these are essentially the only such examples, even for singular Calabi-Yau varieties (Theorem 31). In the smooth case, the answer is especially simple. Theorem 3 Let X be an elliptic Calabi-Yau manifold such that H 2 (X, O X ) = 0. Then every small deformation of X is also an elliptic Calabi-Yau manifold .
Emergent/quantum gravity: macro/micro structures of spacetime

Emergent gravity views spacetime as an entity emergent from a more complete theory of interacting fundamental constituents valid at much finer resolution or higher energies, usually assumed to be above the Planck energy. In this view general relativity is an effective theory valid only at long wavelengths and low energies. We describe the tasks of emergent gravity from any ('top-down') candidate theory for the microscopic structure of spacetime (quantum gravity), namely, identifying the conditions and processes or mechanisms whereby the familiar macroscopic spacetime described by general relativity and matter content described by quantum field theory both emerge with high probability and reasonable robustness. We point out that this task may not be so easy as commonly conjured (as implied in the 'theory of everything') because there are emergent phenomena which cannot simply be deduced from a given micro-theory. Going in the opposite direction ('bottom-up') is the task of quantum gravity, i.e., finding a theory for the microscopic structure of spacetime, which, in this new view, cannot come from quantizing the metric or connection forms because they are the collective variables which are meaningful only for the macroscopic theory (valid below the Planck energy). This task looks very difficult or almost impossible because it entails reconstructing lost information. We point out that the situation may not be so hopeless if we ask the right questions and have the proper tools for what we want to look for. We suggest pathways to move 'up' (in energy) from the given macroscopic conditions of classical gravity and quantum field theory to the domain closer to the micro-macro interface where spacetime emerged and places to look for clues or tell-tale signs at low energy where one could infer indirectly some salient features of the micro-structure of spacetime.
Composite parameterization and Haar measure for all unitary and special unitary groups

We adopt the concept of the composite parameterization of the unitary group U(d) to the special unitary group SU(d). Furthermore, we also consider the Haar measure in terms of the introduced parameters. We show that the well-defined structure of the parameterization leads to a concise formula for the normalized Haar measure on U(d) and SU(d). With regard to possible applications of our results, we consider the computation of high-order integrals over unitary groups.
Loewy series of Weyl modules and the Poincar\'{e} polynomials of quiver varieties

We prove that a Weyl module for the current Lie algebra associated with a simple Lie algebra of type $ADE$ is rigid, that is, it has a unique Loewy series. Further we use this result to prove that the grading on a Weyl module defined by the degree of currents coincides with another grading which comes from the degree of the homology group of the quiver variety. As a corollary we obtain a formula for the Poincar\'{e} polynomials of quiver varieties of type $ADE$ in terms of the energy functions defined on the crystals for tensor products of level-zero fundamental representations of the corresponding quantum affine algebras.
Hilbert-Schauder frame operators

We introduce a new concept of frame operators for Banach spaces we call a HilbertSchauder frame operator. This is a hybird between standard frame theory for Hilbert spaces and Schauder frame theory for Banach spaces. Most of our results involve basic structure properties of the Hilbert-Schauder frame operator. Examples of Hilbert-Schauder frames include standard Hilbert frames and classical bases of p and Lp -spaces with 1 < p 2 . Finally, we give a new isomorphic characterization of Hilbert spaces. Mathematics subject classification (2010): Primary 46B15, 46B28, 46B45, 47B38; Secondary 47A20.
The two bosonizations of the CKP hierarchy: overview and character identities

We discuss the Hirota bilinear equation for the CKP hierarchy introduced by Date, Jimbo, Kashiwara and Miwa in J. Phys. Soc. Japan. 50(11), 3813-3818 (1981), and its algebraic properties. We review in parallel the two bosonizations of the CKP hierarchy: one arising from a twisted Heisenberg algebra (van de Leur, Orlov and Shiota, SIGMA 8, 28 (2012)), and the second from an untwisted Heisenberg algebra (Anguelova, J. Math. Phys. 58(7), 071707 (2017)). In particular, we recount the decompositions into irreducible Heisenberg modules and the (twisted) fermionic structures of the spaces spanned by the highest weight vectors under the two Heisenberg actions. We show that the two bosonizations give rise to four different diagonalizable grading operators on the CKP Fock space, not all of them commuting among each other. We compute the various graded dimensions related to these four grading operators. We prove a sum-vs-product identity relating the bosonic vs fermionic descriptions under the untwisted Heisenberg action, utilizing the charge and the degree grading operators. As a corollary, the resulting identities relate the CKP hierarchy, the Dyson crank of a partition and the Hammond-Lewis birank of a distinct integer bipartition.
Scalp acupuncture for stroke: A protocol for an overview of systematic reviews and meta-analysis

Background: Scalp acupuncture (SA) is a new acupuncture method that connects head acupoints and aculines, and many systematic reviews (SRs) have been published on its use against neuropsychiatric diseases. However, no overview of SRs on the effectiveness of SA in stroke recovery has been conducted. Therefore, our overview aims to evaluate the methodological bias and reliability of the conclusions of SRs regarding SA for stroke recovery and help clinical decision-makers translate this research into clinical policy and practice. Methods: We will consider SRs and meta-analyses of randomized controlled trials to evaluate the effects of SA on stroke recovery. Two reviewers will identify relevant studies, extract data information, and assess the methodological quality using the Assessment of Multiple Systematic Reviews-2 tool. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses report checklist will also be included in the study to assess the quality of the reports. We will use evaluations of the Grading of Recommendations Assessment, Development and Evaluation of the authors of the included SRs. The Risk of Bias in Systematic Review tool will be used to assess the risk of bias of SRs. The screening of SRs, eligibility evaluation, data extraction, methodological quality, and quality of evidence will be conducted by independent reviewers in pairs. The outcomes of interest include the Modified Edinburgh–Scandinavian Stroke Scale, Ability of Daily Living, Functional Independence Measure, Barthel index, Fugl–Meyer assessment, clinical effective rate, and adverse events. Data will be extracted using predefined forms designed to summarize the important characteristics of each review. The evidence will be a descriptive synthesis of the type and content of the intervention and the results reported. Results: The results will be published in a peer-reviewed journal. Conclusions: We expect to organize evidence from multiple SRs on the effectiveness of SA for stroke recovery and synthesize the findings in an accessible and useful documentation.
Experimental Demonstration of Compensation of Beam-Beam Effects by Electron Lenses

We report the first experimental demonstration of compensation of beam-beam interaction effects in high-energy particle collider by using space-charge forces of a low-energy electron beam. In our experiments, an electron lens, a novel instrument developed for the beam-beam compensation, was set on a 980-GeV proton bunch in the Tevatron proton-antiproton collider. The proton bunch losses due to its interaction with antiproton beam were reduced by a factor of 2 when the electron lens was operating. We describe the principle of electron lens operation and present experimental results.