# Top arXiv papers

• Quantum hypothesis testing is one of the most basic tasks in quantum information theory and has fundamental links with quantum communication and estimation theory. In this paper, we establish a formula that characterizes the decay rate of the minimal Type-II error probability in a quantum hypothesis test of two Gaussian states given a fixed constraint on the Type-I error probability. This formula is a direct function of the mean vectors and covariance matrices of the quantum Gaussian states in question. We give an application to quantum illumination, which is the task of determining whether there is a low-reflectivity object embedded in a target region with a bright thermal-noise bath. For the asymmetric-error setting, we find that a quantum illumination transmitter can achieve an error probability exponent much stronger than a coherent-state transmitter of the same mean photon number, and furthermore, that it requires far fewer trials to do so. This occurs when the background thermal noise is either low or bright, which means that a quantum advantage is even easier to witness than in the symmetric-error setting because it occurs for a larger range of parameters. Going forward from here, we expect our formula to have applications in settings well beyond those considered in this paper, especially to quantum communication tasks involving quantum Gaussian channels.
• A subgraph of an edge-coloured complete graph is called rainbow if all its edges have different colours. In 1980 Hahn conjectured that every properly edge-coloured complete graph $K_n$ has a rainbow Hamiltonian path. Although this conjecture turned out to be false, it was widely believed that such a colouring always contains a rainbow cycle of length almost $n$. In this paper, improving on several earlier results, we confirm this by proving that every properly edge-coloured $K_n$ has a rainbow cycle of length $n-O(n^{3/4})$. One of the main ingredients of our proof, which is of independent interest, shows that a random subgraph of a properly edge-coloured $K_n$ formed by the edges of a random set of colours has a similar edge distribution as a truly random graph with the same edge density. In particular it has very good expansion properties.
• In this paper we develop an operational formulation of General Relativity similar in spirit to existing operational formulations of Quantum Theory. To do this we introduce an operational space (or op-space) built out of scalar fields. A point in op-space corresponds to some nominated set of scalar fields taking some given values in coincidence. We assert that op-space is the space in which we observe the world. We introduce also a notion of agency (this corresponds to the ability to set knob settings just like in Operational Quantum Theory). The effects of agents' actions should only be felt to the future so we introduce also a time direction field. Agency and time direction can be understood as effective notions. We show how to formulate General Relativity as a possibilistic theory and as a probabilistic theory. In the possibilistic case we provide a compositional framework for calculating whether some operationally described situation is possible or not. In the probabilistic version we introduce probabilities and provide a compositional framework for calculating the probability of some operationally described situation. Finally we look at the quantum case. We review the operator tensor formulation of Quantum Theory and use it to set up an approach to Quantum Field Theory that is both operational and compositional. Then we consider strategies for solving the problem of Quantum Gravity. By referring only to operational quantities we are able to provide formulations for the possibilistic, probabilistic, and (the nascent) quantum cases that are manifestly invariant under diffeomorphisms.
• The Teff = 20,800 K white dwarf WD 1536+520 is shown to have broadly solar abundances of the major rock forming elements O, Mg, Al, Si, Ca, and Fe, together with a strong relative depletion in the volatile elements C and S. In addition to the highest metal abundances observed to date, including log(O/He) = -3.4, the helium-dominated atmosphere has an exceptional hydrogen abundance at log(H/He) = -1.7. Within the uncertainties, the metal-to-metal ratios are consistent with the accretion of an H2O-rich and rocky parent body, an interpretation supported by the anomalously high trace hydrogen. The mixed atmosphere yields unusually short diffusion timescales for a helium atmosphere white dwarf, of no more than a few hundred yr, and equivalent to those in a much cooler, hydrogen-rich star. The overall heavy element abundances of the disrupted parent body deviate modestly from a bulk Earth pattern, and suggest the deposition of some core-like material. The total inferred accretion rate is 4.2e9 g/s, and at least 4 times higher than any white dwarf with a comparable diffusion timescale. Notably, when accretion is exhausted in this system, both metals and hydrogen will become undetectable within roughly 300 Myr, thus supporting a scenario where the trace hydrogen is related to the ongoing accretion of planetary debris.
• We report on the evidence for the multiband electronic transport in $\alpha$-YbAlB$_{4}$ and $\alpha$-Yb$_{0.81(2)}$Sr$_{0.19(3)}$AlB$_{4}$. Multiband transport reveals itself below 10 K in both compounds via Hall effect measurements, whereas anisotropic magnetic ground state sets in below 3 K in $\alpha$-Yb$_{0.81(2)}$Sr$_{0.19(3)}$AlB$_{4}$. Our results show that Sr$^{2+}$ substitution enhances conductivity, but does not change the quasiparticle mass of bands induced by heavy fermion hybridization.
• In this paper, we study the inviscid limit of the free surface incompressible Navier-Stokes equations with or without surface tension. By delicate estimates, we prove the weak boundary layer of the velocity of the free surface Navier-Stokes equations and the existence of strong or weak vorticity layer for different conditions. When the limit of the difference between the initial Navier-Stokes vorticity and the initial Euler vorticity is nonzero, or the tangential projection on the free surface of the Euler strain tensor multiplying by normal vector is nonzero, there exists a strong vorticity layer. Otherwise, the vorticity layer is weak. We estimate convergence rates of tangential derivatives and the first order standard normal derivative in energy norms, we show that not only tangential derivatives and standard normal derivative have different convergence rates, but also their convergence rates are different for different Euler boundary data. Moreover, we determine regularity structure of the free surface Navier-Stokes solutions with or without surface tension, surface tension changes regularity structure of the solutions.
• This paper presents an algebraic formulation of the renormalization group flow in quantum mechanics on flat target spaces. For any interacting quantum mechanical theory, the fixed point of this flow is a theory of classical probability, not a different effective quantum mechanics. Each energy eigenstate of the UV Hamiltonian flows to a probability distribution whose entropy is a natural diagnostic of quantum ergodicity of the original state. These conclusions are supported by various examples worked out in detail.
• Renormalization group equations are an essential tool for the description of theories accross different energy scales. Even though their expressions at two-loop for an arbitrary gauge field theory have been known for more than thirty years, deriving the full set of equations for a given model by hand is very challenging and prone to errors. To tackle this issue, we have introduced in [1] a Python tool called PyR@TE; Python Renormalization group equations @ Two-loop for Everyone. With PyR@TE, it is easy to implement a given Lagrangian and derive the complete set of two-loop RGEs for all the parameters of the theory. In this paper, we present the new version of this code, PyR@TE 2, which brings many new features and in particular it incorporates kinetic mixing when several $\mathrm{U}(1)$ gauge groups are involved. In addition, the group theory part has been greatly improved as we introduced a new Python module dubbed PyLie that deals with all the group theoretical aspects required for the calculation of the RGEs as well as providing very useful model building capabilities. This allows the use of any irreducible representation of the $\mathrm{SU}(n)$, $\mathrm{SO}(2n)$ and $\mathrm{SO(2n+1)}$ groups. % Furthermore, it is now possible to implement terms in the Lagrangian involving fields which can be contracted into gauge singlets in more than one way. As a byproduct, results for a popular model (SM+complex triplet) for which, to our knowledge, the complete set of two-loop RGEs has not been calculated before are presented in this paper. Finally, the two-loop RGEs for the anomalous dimension of the scalar and fermion fields have been implemented as well. It is now possible to export the coupled system of beta functions into a numerical C++ function, leading to a consequent speed up in solving them.
• Microwave heating of a high-temperature plasma confined in a large-scale open magnetic trap, including all important wave effects like diffraction, absorption, dispersion and wave beam aberrations, is described for the first time within the first-principle technique based on consistent Maxwell's equations. With this purpose, the quasi-optical approach is generalized over weakly inhomogeneous gyrotrotropic media with resonant absorption and spatial dispersion, and a new form of the integral quasi-optical equation is proposed. An effective numerical technique for this equation's solution is developed and realized in a new code QOOT, which is verified with the simulations of realistic electron cyclotron heating scenarios at the Gas Dynamic Trap at the Budker Institute of Nuclear Physics (Novosibirsk, Russia).
• Gieseker-Nakajima moduli spaces $M_{k}(n)$ parametrize the charge $k$ noncommutative $U(n)$ instantons on ${\bf R}^{4}$ and framed rank $n$ torsion free sheaves $\mathcal{E}$ on ${\bf C\bf P}^{2}$ with ${\rm ch}_{2}({\mathcal{E}}) = k$. They also serve as local models of the moduli spaces of instantons on general four-manifolds. We study the generalization of gauge theory in which the four dimensional spacetime is a stratified space $X$ immersed into a Calabi-Yau fourfold $Z$. The local model ${\bf M}_{k}({\vec n})$ of the corresponding instanton moduli space is the moduli space of charge $k$ (noncommutative) instantons on origami spacetimes. There, $X$ is modelled on a union of (up to six) coordinate complex planes ${\bf C}^{2}$ intersecting in $Z$ modelled on ${\bf C}^{4}$. The instantons are shared by the collection of four dimensional gauge theories sewn along two dimensional defect surfaces and defect points. We also define several quiver versions ${\bf M}_{\bf k}^{\gamma}({\vec{\bf n}})$ of ${\bf M}_{k}({\vec n})$, motivated by the considerations of sewn gauge theories on orbifolds ${\bf C}^{4}/{\Gamma}$. The geometry of the spaces ${\bf M}_{\bf k}^{\gamma}({\vec{\bf n}})$, more specifically the compactness of the set of torus-fixed points, for various tori, underlies the non-perturbative Dyson-Schwinger identities recently found to be satisfied by the correlation functions of $qq$-characters viewed as local gauge invariant operators in the ${\mathcal{N}}=2$ quiver gauge theories. The cohomological and K-theoretic operations defined using ${\bf M}_{k}({\vec n})$ and their quiver versions as correspondences provide the geometric counterpart of the $qq$-characters, line and surface defects.
• Kinetic mixing is a fundamental property of models with a gauge symmetry involving several $\mathrm{U}(1)$ group factors. In this paper, we perform a numerical study of the impact of kinetic mixing on beta functions at two-loop. To do so, we use the recently published PyR@TE 2 software to derive the complete set of RGEs of the SM B-L model at two-loop including kinetic mixing. We show that it is important to properly account for kinetic mixing as the evolution of the parameters with the energy scale can change drastically. In some cases, these modifications can even lead to a different conclusion regarding the stability of the scalar potential.
• The best previous lower bounds for kissing numbers in dimensions 25 through 31 were constructed using a set $S$ with $|S| = 480$ of minimal vectors of the Leech Lattice, $\Lambda_{24}$, such that $\langle x, y \rangle \leq 1$ for any distinct $x, y \in S$. Then, a probabilistic argument based on applying automorphisms of $\Lambda_{24}$ gives more disjoint sets $S_i$ of minimal vectors of $\Lambda_{24}$ with the same property. Cohn, Jiao, Kumar, and Torquato proved that these subsets give kissing configurations in dimensions 25 through 31 of given size linear in the sizes of the subsets. We achieve $|S| = 488$ by applying simulated annealing. We also improve the aforementioned probabilistic argument in the general case. Finally, we greedily construct even larger $S_i$'s given our $S$ of size $488$, giving increased lower bounds on kissing numbers in $\mathbb{R}^{25}$ through $\mathbb{R}^{31}$.
• The classical part of the QCD partition function (the integrand) has, ignoring irrelevant exact zero modes of the Dirac operator, a local SU(2N_F) ⊃SU(N_F)_L \times SU(N_F)_R \times U(1)_A symmetry which is absent at the Lagrangian level. This symmetry is broken anomalously and spontaneously. Effects of spontaneous breaking of chiral symmetry are contained in the near-zero modes of the Dirac operator. If physics of anomaly is also encoded in the same near-zero modes, then their truncation on the lattice should recover a hidden classical SU(2N_F) symmetry in correlators and spectra. This naturally explains observation on the lattice of a large degeneracy of hadrons, that is higher than the SU(N_F)_L \times SU(N_F)_R \times U(1)_A chiral symmetry, upon elimination by hands of the lowest-lying modes of the Dirac operator. We also discuss an implication of this symmetry for the high temperature QCD.
• In this paper, we present a new multiscale model reduction technique for the Stokes flows in heterogeneous perforated domains. The challenge in the numerical simulations of this problem lies in the fact that the solution contains many multiscale features and requires a very fine mesh to resolve all details. In order to efficiently compute the solutions, some model reductions are necessary. To obtain a reduced model, we apply the generalized multiscale finite element approach, which is a framework allowing systematic construction of reduced models. Based on this general framework, we will first construct a local snapshot space, which contains many possible multiscale features of the solution. Using the snapshot space and a local spectral problem, we identify dominant modes in the snapshot space and use them as the multiscale basis functions. Our basis functions are constructed locally with non-overlapping supports, which enhances the sparsity of the resulting linear system. In order to enforce the mass conservation, we propose a hybridized technique, and uses a Lagrange multiplier to achieve mass conservation. We will mathematically analyze the stability and the convergence of the proposed method. In addition, we will present some numerical examples to show the performance of the scheme. We show that, with a few basis functions per coarse region, one can obtain a solution with excellent accuracy.
• We present measurements of the reduction of light output by plastic scintillators irradiated in the CMS detector during the 8 TeV run of the Large Hadron Collider and show that they indicate a strong dose rate effect. The damage for a given dose is larger for lower dose rate exposures. The results agree with previous measurements of dose rate effects, but are stronger due to the very low dose rates probed. We show that the scaling with dose rate is consistent with that expected from diffusion effects.
• We experimentally investigate the dynamics of particle rearrangements for a 2D Brownian colloidal suspension under cyclic shear. We find that, even though the system is liquid-like and non-rigid ($\phi\leq0.32$), a fraction of particles undergo reversible cycles, in the form of scattered particle clusters. Unlike jammed athermal systems, the reversible clusters are not stable and the particles transition between reversible and irreversible cycles. We demonstrate that the stability of reversibility depends both on $\phi$ and strain amplitude. We also identify plastic reversibility for our thermal system. However, as $\phi$ is decreased deep into liquid phase, the hysterysis in particle rearrangements becomes less prominent, and the dynamics is moved closer to equilibrium by thermal noise.
• It is known that the Painleve VI is obtained by connection preserving deformation of some linear differential equations, and the Heun equation is obtained by a specialization of the linear differential equations. We inverstigate degenerations of the Ruijsenaars-van Diejen difference opearators and show difference analogues of the Painleve-Heun correspondence.
• Proxima Centauri b, an Earth-size planet in the habitable zone of our nearest stellar neighbour, has just been discovered. A theoretical framework of synchronously rotating planets, in which the risk of a runaway greenhouse on the sunlight side and atmospheric collapse on the reverse side are mutually ameliorated via heat transport is discussed. This is developed via simple (tutorial) models of the climate. These show that lower incident stellar flux means that less heat transport, so less atmospheric mass, is required. The incident stellar flux at Proxima Centauri b is indeed low, which may help enhance habitability if it has suffered some atmospheric loss or began with a low volatile inventory.
• In this paper we discuss the boson/vortex duality by mapping the Gross-Pitaevskii theory into an effective string theory, both with and without boundaries. Through the effective string theory, we find the Seiberg-Witten map between the commutative and the noncommutative tachyon field theories, and consequently identify their soliton solutions with the D-branes in the effective string theory. We perform various checks of the duality map and the identification of classical solutions. This new insight of the duality between the Gross-Pitaevskii theory and the effective string theory allows us to test many results of string theory in Bose-Einstein condensates, and at the same time help us understand the quantum behavior of superfluids and cold atom systems.
• We present a type system and inference algorithm for a rich subset of JavaScript equipped with objects, structural subtyping, prototype inheritance, and first-class methods. The type system supports abstract and recursive objects, and is expressive enough to accommodate several standard benchmarks with only minor workarounds. The invariants enforced by the types enable an ahead-of-time compiler to carry out optimizations typically beyond the reach of static compilers for dynamic languages. Unlike previous inference techniques for prototype inheritance, our algorithm uses a combination of lower and upper bound propagation to infer types and discover type errors in all code, including uninvoked functions. The inference is expressed in a simple constraint language, designed to leverage off-the-shelf fixed point solvers. We prove soundness for both the type system and inference algorithm. An experimental evaluation showed that the inference is powerful, handling the aforementioned benchmarks with no manual type annotation, and that the inferred types enable effective static compilation.
• Let $G = (N,E,w)$ be a weighted communication graph (with weight function $w$ on $E$). For every subset $A \subseteq N$, we delete in the subset $E(A)$ of edges with ends in $A$, all edges of minimum weight in $E(A)$. Then the connected components of the corresponding induced subgraph constitute a partition of $A$ that we call $P_{\min}(A)$. For every game $(N, v)$, we define the $P_{\min}$-restricted game $(N, \bar{v})$ by $\bar{v}(A) = \sum_{F \in P_{\min}(A)} v(F)$ for all $A \subseteq N$. We prove that we can decide in polynomial time if there is inheritance of $\mathcal{F}$-convexity from $(N, v)$ to the $P_{\min}$-restricted game $(N, \bar{v})$ where $\mathcal{F}$-convexity is obtained by restricting convexity to connected subsets.
• Phosphorylation, the enzyme-mediated addition of a phosphate group to a molecule, is a ubiquitous chemical mechanism in biology. Multisite phosphorylation, the addition of phosphate groups to multiple sites of a single molecule, may be distributive or processive. Distributive systems can be bistable, while processive systems were recently shown to be globally stable. However, this global convergence result was proven only for a specific mechanism of processive phosphorylation/dephosphorylation (namely, all catalytic reactions are reversible). Accordingly, we generalize this result to allow for processive phosphorylation networks in which each reaction may be irreversible, and also to account for possible product inhibition. We accomplish this by defining an all-encompassing processive network that encapsulates all of these schemes, and then appealing to recent results of Marcondes de Freitas, Wiuf, and Feliu that assert global convergence by way of monontone systems theory and network/graph reductions (which correspond to removal of intermediate complexes). Our results form a case study into the question of when global convergence is preserved when reactions and/or intermediate complexes are added to or removed from a network.
• Let $T$ be an $m$-interval exchange transformation. By the rank of $T$ we mean the dimension of the $\mathbb{Q}$-vector space spanned by the lengths of the exchanged subintervals. We prove that if $T$ satisfies Keane's infinite distinct orbit condition and $\text{rank}(T)>1+\lfloor m/2 \rfloor$ then the only interval exchange transformations which commute with $T$ are its powers. The main step in our proof is to show that the centralizer of $T$ is torsion-free under the above hypotheses.
• An ontology of Leibnizian relationalism, consisting in distance relations among sparse matter points and their change only, is well recognized as a serious option in the context of classical mechanics. In this paper, we investigate how this ontology fares when it comes to general relativistic physics. Using a Humean strategy, we regard the gravitational field as a means to represent the overall change in the distance relations among point particles in a way that achieves the best combination of being simple and being informative.
• Among solutions of the strong CP problem, the "invisible" axion in the narrow axion window is argued to be the remaining possibility among natural solutions on the smallness of $\bar{\theta}$. Related to the gravity spoil of global symmetries, some prospective invisible axions from theory point of view are discussed. In all these discussions, including the observational possibility, cosmological constraints must be included.
• For any acyclic directed graph $G$, we introduce two notions: one is called an upward planar order on $G$ which is a linear extension of the edge poset of $G$ with some constraints, the other is called a canonical progressive planar extension (CPP extension for short) of $G$ which is an embedding of $G$ into a progressive planar graph with some constraints. Based on new characterizations of progressive planar graphs, we show that there is a natural bijection between the set of upward planar orders of $G$ and the set of CPP extensions of $G$. Finally we justify the combinatorial definition that an upward planar graph is an acyclic directed graph with an upward planar order.
• The self-assembly of partially wet hexagonal-disk monolayers under vertical vibrations is investigated experimentally. Due to the formation of liquid bridges, the disks are subjected to short-ranged attractive interactions. Unlike spheres, hexagonal disks prefer to spin upon sufficiently strong driving. Consequently, a rotator-crystal state with the disks self-organized in a hexagonal structure dominates over a wide range of vibration strength. The bond length of the rotator-crystals is slightly smaller than the diameter of the circumscribed circle of a hexagon, indicating geometric frustration. An analysis of the mobility of a single disk reveals that the preference to spin arises from the broken circular symmetry. This investigation provides an example where the collective behavior of granular matter is tuned by the shape of individual particles.
• We introduce a novel latent vector space model that jointly learns the latent representations of words, e-commerce products and a mapping between the two without the need for explicit annotations. The power of the model lies in its ability to directly model the discriminative relation between products and a particular word. We compare our method to existing latent vector space models (LSI, LDA and word2vec) and evaluate it as a feature in a learning to rank setting. Our latent vector space model achieves its enhanced performance as it learns better product representations. Furthermore, the mapping from words to products and the representations of words benefit directly from the errors propagated back from the product representations during parameter estimation. We provide an in-depth analysis of the performance of our model and analyze the structure of the learned representations.
• Direct detection and spectroscopy of exoplanets requires high contrast imaging. For habitable exoplanets in particular, located at small angular separation from the host star, it is crucial to employ small inner working angle (IWA) coronagraphs that efficiently suppress starlight. These coronagraphs, in turn, require careful control of the wavefront which directly impacts their performance. For ground-based telescopes, atmospheric refraction is also an important factor, since it results in a smearing of the PSF, that can no longer be efficiently suppressed by the coronagraph. Traditionally, atmospheric refraction is compensated for by an atmospheric dispersion compensator (ADC). ADC control relies on an a priori model of the atmosphere whose parameters are solely based on the pointing of the telescope, which can result in imperfect compensation. For a high contrast instrument like the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system, which employs very small IWA coronagraphs, refraction-induced smearing of the PSF has to be less than 1 mas in the science band for optimum performance. In this paper, we present the first on-sky measurement and correction of residual atmospheric dispersion. Atmospheric dispersion is measured from the science image directly, using an adaptive grid of artificially introduced speckles as a diagnostic to feedback to the telescope's ADC. With our current setup, we were able to reduce the initial residual atmospheric dispersion from 18.8 mas to 4.2 in broadband light (y- to H-band), and to 1.4 mas in H-band only. This work is particularly relevant to the upcoming extremely large telescopes (ELTs) that will require fine control of their ADC to reach their full high contrast imaging potential.
• We study dynamically crowded solutions of stiff fibers deep in the semidilute regime, where the motion of a single constituent becomes increasingly confined to a narrow tube. The spatiotemporal dynamics for wave numbers resolving the motion in the confining tube becomes accessible in Brownian dynamics simulations upon employing a geometry-adapted neighbor list. We demonstrate that in such crowded environments the intermediate scattering function, characterizing the motion in space and time, can be predicted quantitatively by simulating a single freely diffusing phantom needle only, yet with very unusual diffusion coefficients.
• Deep learning has been shown as a successful machine learning method for a variety of tasks, and its popularity results in numerous open-source deep learning software tools coming to public. Training a deep network is usually a very time-consuming process. To address the huge computational challenge in deep learning, many tools exploit hardware features such as multi-core CPUs and many-core GPUs to shorten the training time. However, different tools exhibit different features and running performance when training different types of deep networks on different hardware platforms, which makes it difficult for end users to select an appropriate pair of software and hardware. In this paper, we aim to make a comparative study of the state-of-the-art GPU-accelerated deep learning software tools, including Caffe, CNTK, TensorFlow, and Torch. We benchmark the running performance of these tools with three popular types of neural networks on two CPU platforms and three GPU platforms. Our contribution is two-fold. First, for deep learning end users, our benchmarking results can serve as a guide to selecting appropriate software tool and hardware platform. Second, for deep learning software developers, our in-depth analysis points out possible future directions to further optimize the training performance.
• We study the monopole (breathing) mode of a finite temperature Bose-Einstein condensate in an isotropic harmonic trap recently developed by D.~S.~Lobser et al. [Nat.~Phys., \textbf11, 1009 (2015)]. We observe a non-exponential collapse of the amplitude of the condensate oscillation followed by a partial revival. This behavior is identified as being due to beating between two eigenmodes of the system, corresponding to in-phase and out-of-phase oscillations of the condensed and non-condensed fractions of the gas. We perform finite temperature simulations of the system dynamics using the Zaremba-Nikuni-Griffin methodology [J.~Low Temp.~Phys., \textbf116, 277 (1999)], and find good agreement with the data, thus confirming the two mode description.
• We consider the minimal number of points on a regular grid on the plane that generates n blocks of points of exactly length k and show that this number is upper bounded by kn/3 and approaches kn/4 as $n\rightarrow\infty$ when k+1 is coprime with 6 or when k is large.
• Previous realizations of synthetic gauge fields for ultracold atoms do not allow the spatial profile of the field to evolve freely. We propose a scheme which overcomes this restriction by using the light in a multimode cavity, in conjunction with Raman coupling, to realize an artificial magnetic field which acts on a Bose-Einstein condensate of neutral atoms. We describe the evolution of such a system, and present the results of numerical simulations which show dynamical coupling between the effective field and the matter on which it acts. Crucially, the freedom of the spatial profile of the field is sufficient to realize a close analogue of the Meissner effect, where the magnetic field is expelled from the superfluid. This back-action of the atoms on the synthetic field distinguishes the Meissner-like effect described here from the Hess-Fairbank suppression of rotation in a neutral superfluid observed elsewhere.
• In a recent study, we reported the results of a new decision making paradigm in which the participants were asked to balance between their speed and accuracy to maximize the total reward they achieve during the experiment. The results of computational modeling provided strong evidence suggesting that the participants used time-varying decision boundaries. Previous theoretical studies of the optimal speed-accuracy trade-off suggested that the participants may learn to use these time-varying boundaries to maximize their average reward rate. The results in our experiment, however, showed that the participants used such boundaries even at the beginning of the experiment and without any prior experience in the task. In this paper, we hypothesize that these boundaries are the results of using some heuristic rules to make decisions in the task. To formulate decision making by these heuristic rules as a computational framework, we use the fuzzy logic theory. Based on this theory, we propose a new computational framework for decision making in evidence accumulation tasks. In this framework, there is no explicit decision boundary. Instead, the subject's desire to stop accumulating evidence and responding at each moment within a trial and for a given value of the accumulated evidence, is determined by a set of fuzzy "IF-TEHN rules". We then use the back-propagation method to derive an algorithm for fitting the fuzzy model to each participant's data. We then investigate how the difference in the participants' performance in the experiment is reflected in the difference in the parameters of the fitted model
• It is natural to investigate if the quantization of an integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of natural Hamiltonians with constants of motion quadratic in the momenta. The procedure of quantization here considered, transforms the Hamiltonian into the Laplace-Beltrami operator plus a scalar potential. In order to transform the constants of motion into symmetry operators of the quantum Hamiltonian, additional scalar potentials, known as quantum corrections, must be introduced, depending on the Riemannian structure of the manifold. We give here a complete geometric characterization of the quantum corrections necessary for the case considered. Stäckel systems are studied in particular details. Examples in conformally and non-conformally flat manifolds are given.
• We present an online visual tracking algorithm by managing multiple target appearance models in a tree structure. The proposed algorithm employs Convolutional Neural Networks (CNNs) to represent target appearances, where multiple CNNs collaborate to estimate target states and determine the desirable paths for online model updates in the tree. By maintaining multiple CNNs in diverse branches of tree structure, it is convenient to deal with multi-modality in target appearances and preserve model reliability through smooth updates along tree paths. Since multiple CNNs share all parameters in convolutional layers, it takes advantage of multiple models with little extra cost by saving memory space and avoiding redundant network evaluations. The final target state is estimated by sampling target candidates around the state in the previous frame and identifying the best sample in terms of a weighted average score from a set of active CNNs. Our algorithm illustrates outstanding performance compared to the state-of-the-art techniques in challenging datasets such as online tracking benchmark and visual object tracking challenge.
• The technique of Formal Concept Analysis is applied to a dataset describing the traits of rodents, with the goal of identifying zoonotic disease carriers,or those species carrying infections that can spillover to cause human disease. The concepts identified among these species together provide rules-of-thumb about the intrinsic biological features of rodents that carry zoonotic diseases, and offer utility for better targeting field surveillance efforts in the search for novel disease carriers in the wild.
• We utilise the theory of crossed simplicial groups to introduce a collection of Quillen model structures on the category of simplicial presheaves with a compact planar Lie group action on a small Grothendieck site.
• Graviton loop corrections to observables in de Sitter space often lead to infrared divergences. We show that these infrared divergences are resolved by the spontaneous breaking of de Sitter invariance.
• Aug 26 2016 math.NT arXiv:1608.07236v1
We define a derived version of Mazur's Galois deformation ring. It is a pro-simplicial ring $\mathcal{R}$ classifying deformations of a fixed Galois representation to simplicial coefficient rings; its zeroth homotopy group $\pi_0 \mathcal{R}$ recovers Mazur's deformation ring. We give evidence that these rings $\mathcal{R}$ occur in the wild: For suitable Galois representations, the Langlands program predicts that $\pi_0 \mathcal{R}$ should act on the homology of an arithmetic group. We explain how the Taylor--Wiles method can be used to upgrade such an action to a graded action of $\pi_* \mathcal{R}$ on the homology.
• We present a self-contained operator-based approach to derive the spectrum of trapped ions. This approach provides the complete normal form of the low energy quadratic Hamiltonian in terms of bosonic phonons, as well as an effective free particle degree of freedom for each spontaneously broken spatial symmetry. We demonstrate how this formalism can directly be used to characterize an ion chain both in the linear and the zigzag regimes. In particular we compute, both for the ground state and finite temperature states, spatial correlations, heat capacity and dynamical susceptibility. Last, for the ground state which has quantum correlations, we analyze the amount of energy reduction compared to an uncorrelated state with minimum energy, thus highlighting how the system can lower its energy by correlations.
• We describe a graded extension of the usual Hecke algebra: it acts in a graded fashion on the cohomology of an arithmetic group $\Gamma$. Under favorable conditions, the cohomology is freely generated in a single degree over this graded Hecke algebra. From this construction we extract an action of certain $p$-adic Galois cohomology groups on $H^*(\Gamma, \mathbb{Q}_p)$, and formulate the central conjecture: the motivic $\mathbb{Q}$-lattice inside these Galois cohomology groups preserves $H^*(\Gamma,\mathbb{Q})$.
• The Griffiths phase has been proposed to induce a stretched critical regime that facilitates self organizing of brain networks for optimal function. This phase stems from the intrinsic structural heterogeneity of brain networks, such as the hierarchical modular structure. In this work, we extend this concept to modified hierarchical networks with small-world connections based on Hanoi networks [1]. Through extensive simulations, we identify the essential role played by the exponential distribution of the inter-moduli connectivity probability across hierarchies on the emergence of the Griffiths phase in this network. Additionally, the spectral analysis on the adjacency matrix of the relevant networks [2] shows that a localized principle eigenvector is not necessarily the fingerprint of the Griffiths phase.
• Recent observations suggest ongoing planet formation in the innermost parsec of the Galactic center (GC). The super-massive black hole (SMBH) might strip planets or planetary embryos from their parent star, bringing them close enough to be tidally disrupted. Photoevaporation by the ultraviolet field of young stars, combined with ongoing tidal disruption, could enhance the near-infrared luminosity of such starless planets, making their detection possible even with current facilities. In this paper, we investigate the chance of planet tidal captures by means of high-accuracy N-body simulations exploiting Mikkola's algorithmic regularization. We consider both planets lying in the clockwise (CW) disk and planets initially bound to the S-stars. We show that tidally captured planets remain on orbits close to those of their parent star. Moreover, the semi-major axis of the planet orbit can be predicted by simple analytic assumptions in the case of prograde orbits. We find that starless planets that were initially bound to CW disk stars have mild eccentricities and tend to remain in the CW disk. However, we speculate that angular momentum diffusion and scattering with other young stars in the CW disk might bring starless planets on low-angular momentum orbits. In contrast, planets initially bound to S-stars are captured by the SMBH on highly eccentric orbits, matching the orbital properties of the G1 and G2 clouds. Our predictions apply not only to planets but also to low-mass stars initially bound to the S-stars and tidally captured by the SMBH.
• Aug 26 2016 math.MG arXiv:1608.07229v1
We introduce a notion of a sub-Moebius structure and find necessary and sufficient conditions under which a sub-Moebius structure is a Moebius structure. We show that on the boundary at infinity of every Gromov hyperbolic space Y there is a canonical sub-Moebius structure which is invariant under isometries of Y such that the sub-Moebius topology on the boundary coincides with the standard one.
• We prove an analogue of the Lebesgue decomposition for continuous functionals on the commutant modulo a reflexive normed ideal of an n-tuple of hermitian operators for which there are quasicentral approximate units relative to the normed ideal. Using results of Godefroy-Talagrand and Pfitzner we derive from this strong uniqueness of the predual of such a commutant modulo a normed ideal.
• We consider the conformally invariant cubic wave equation on the Einstein cylinder $\mathbb{R} \times \mathbb{S}^3$ for small rotationally symmetric initial data. This simple equation captures many key challenges of nonlinear wave dynamics in confining geometries, while a conformal transformation relates it to a self-interacting conformally coupled scalar in four-dimensional anti-de Sitter spacetime (AdS$_4$) and connects it to various questions of AdS stability. We construct an effective infinite-dimensional time-averaged dynamical system accurately approximating the original equation in the weak field regime. It turns out that this effective system, which we call the \emphconformal flow, exhibits some remarkable features, such as low-dimensional invariant subspaces, a wealth of stationary states (for which energy does not flow between the modes), as well as solutions with nontrivial exactly periodic energy flows. Based on these observations and close parallels to the cubic Szegő equation, which was shown by Gérard and Grellier to be Lax-integrable, it is tempting to conjecture that the conformal flow and the corresponding weak field dynamics in AdS$_4$ are integrable as well.
• In this paper we investigate the hedging problem of a defaultable claim with recovery at default time via the local risk-minimization approach when investors have a restricted information on the market. We assume that the stock price process dynamics depends on an exogenous unobservable stochastic factor and that at any time, investors may observe the risky asset price and know if default has occurred or not. We characterize the optimal strategy in terms of the integrand in the Galtchouk-Kunita-Watanabe decomposition of the defaultable claim with respect to the minimal martingale measure and the available information flow. Finally, we provide an explicit formula by means of predictable projection of the corresponding hedging strategy under full information with respect to the natural filtration of the risky asset price and the minimal martingale measure in a Markovian setting via filtering.
• Gender differences in collaborative research have received little attention when compared with the growing importance that women hold in academia and research. Unsurprisingly, most of bibliometric databases have a strong lack of directly available information by gender. Although empirical-based network approaches are often used in the study of research collaboration, the studies about the influence of gender dissimilarities on the resulting topological outcomes are still scarce. Here, networks of scientific subjects are used to characterize patterns that might be associated to five categories of authorships which were built based on gender. We find enough evidence that gender imbalance in scientific authorships brings a peculiar trait to the networks induced from papers published in Web of Science (WoS) indexed journals of Economics over the period 2010-2015 and having at least one author affiliated to a Portuguese institution. Our results show the emergence of a specific pattern when the network of co-occurring subjects is induced from a set of papers exclusively authored by men. Such a male-exclusive authorship condition is found to be the solely responsible for the emergence that particular shape in the network structure. This peculiar trait might facilitate future network analyses of research collaboration and interdisciplinarity.

resodiat Aug 23 2016 13:00 UTC

That is really a long-term perspective.

Marco Piani Aug 22 2016 22:08 UTC

Born in Italy, and now living in Scotland: I have no excuses not to feel inspired :-)

Māris Ozols Aug 22 2016 18:50 UTC

It is not just in Scotland but in fact across the whole of UK and even beyond. I just found a reference, dating back to the very birth of quantum computing, where the early pioneers [already admit][1] that their work was inspired by Rabezzana Grignolino d'Asti.

[1]: https://scirate.com/arxiv/quan

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JRW Aug 18 2016 16:42 UTC

A video of a talk I gave this morning will be [here][1], if it ever finishes uploading.

[1]: https://youtu.be/I8cMY0AmIY0

Jonathan Oppenehim Jul 28 2016 16:41 UTC

Hi, sorry to just be updating this discussion now -- my conversation with Renato seemed to me to have converged here (and also continued via email and in person and I never updated scirate). However, a few people have asked what the outcome of our discussion was. So let me just say, that yes, my vie

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Valentin Zauner-Stauber Jul 18 2016 09:54 UTC

Conjugate Gradient IS a Krylov-space method...

Renato Renner Jul 09 2016 06:29 UTC

I am afraid that you may have misunderstood my previous answer. I did not at all mean to claim that we *cannot* apply QM to brains. Rather, my point was that F1, after she prepared the electron, *doesn't need to* include her own brain in her analysis (especially because she will no longer interact w

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Tony Sudbery Jul 08 2016 19:25 UTC

Where is it written that quantum mechanics cannot be applied to brains? And if it is so written, how is it possible to have measurements like those that you assign to Wigner and his assistant? Indeed, we don't (yet) apply QM to our brains, because we don't have sufficient knowledge or computing powe

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Renato Renner Jul 08 2016 06:07 UTC

I completely agree with your analysis, which describes the gedankenexperiment from a global (“outside”) perspective, according to the laws of Bohmian Mechanics (BM). And, indeed, it shows that the "memory" of a measurement outcome cannot assumed to be permanent, i.e., it may change (according to BM)

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Tony Sudbery Jul 02 2016 19:09 UTC

Roger Colbeck drew our attention to this paper in the York QFIT group, and we met to discuss it last week. I would like to comment on the relation of Bohmian quantum mechanics to the extended Wigner's friend experiment. As generalised by John Bell, Bohmian qm can be applied to this experiment to yie

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