# Top arXiv papers

• The class $\MIP^*$ of promise problems that can be decided through an interactive proof system with multiple entangled provers provides a complexity-theoretic framework for the exploration of the nonlocal properties of entanglement. Little is known about the power of this class. The only proposed approach for establishing upper bounds is based on a hierarchy of semidefinite programs introduced independently by Pironio et al. and Doherty et al. This hierarchy converges to a value that is only known to coincide with the provers' maximum success probability in a given proof system under a plausible but difficult mathematical conjecture, Connes' embedding conjecture. No bounds on the rate of convergence are known. We introduce a rounding scheme for the hierarchy, establishing that any solution to its $N$-th level can be mapped to a strategy for the provers in which measurement operators associated with distinct provers have pairwise commutator bounded by $O(\ell^2/\sqrt{N})$ in operator norm, where $\ell$ is the number of possible answers per prover. Our rounding scheme motivates the introduction of a variant of $\MIP^*$, called $\MIP_\delta^*$, in which the soundness property is required to hold as long as the commutator of operations performed by distinct provers has norm at most $\delta$. Our rounding scheme implies the upper bound $\MIP_\delta^* \subseteq \DTIME(\exp(\exp(\poly)/\delta^2))$. In terms of lower bounds we establish that $\MIP^*_{2^{-\poly}}$, with completeness $1$ and soundness $1-2^{-\poly}$, contains $\NEXP$. The relationship of $\MIP_\delta^*$ to $\MIPstar$ has connections with the mathematical literature on approximate commutation. Our rounding scheme gives an elementary proof that the Strong Kirchberg Conjecture implies that $\MIPstar$ is computable. We discuss applications to device-independent cryptography.
• We develop a framework for resource efficient compilation of higher-level programs into lower-level reversible circuits. Our main focus is on optimizing the memory footprint of the resulting reversible networks. This is motivated by the limited availability of qubits for the foreseeable future. We apply three main techniques to keep the number of required qubits small when computing classical, irreversible computations by means of reversible networks: first, wherever possible we allow the compiler to make use of in-place functions to modify some of the variables. Second, an intermediate representation is introduced that allows to trace data dependencies within the program, allowing to clean up qubits early. This realizes an analog to "garbage collection" for reversible circuits. Third, we use the concept of so-called pebble games to transform irreversible programs into reversible programs under space constraints, allowing for data to be erased and recomputed if needed. We introduce REVS, a compiler for reversible circuits that can translate a subset of the functional programming language F# into Toffoli networks which can then be further interpreted for instance in LIQui|>, a domain-specific language for quantum computing and which is also embedded into F#. We discuss a number of test cases that illustrate the advantages of our approach including reversible implementations of SHA-2 and other cryptographic hash-functions, reversible integer arithmetic, as well as a test-bench of combinational circuits used in classical circuit synthesis. Compared to Bennett's method, REVS can reduce space complexity by a factor of $4$ or more, while having an only moderate increase in circuit size as well as in the time it takes to compile the reversible networks.
• Living organisms capitalize on their ability to predict their environment to maximize their available free energy, and invest this energy in turn to create new complex structures. Is there a preferred method by which this manipulation of structure should be done? Our intuition is "simpler is better," but this is only a guiding principal. Here, we substantiate this claim through thermodynamic reasoning. We present a new framework for the manipulation of patterns (structured sequences of data) by predictive devices. We identify the dissipative costs and how they can be minimized by the choice of memory in these predictive devices. For pattern generation, we see that simpler is indeed better. However, contrary to intuition, when it comes to extracting work from a pattern, any device capable of making statistically accurate predictions can recover all available energy.
• Oct 02 2015 quant-ph arXiv:1510.00219v1
We propose a method to detect lower bounds to quantum capacities of a noisy quantum communication channel by means of few measurements. The method is easily implementable and does not require any knowledge about the channel. We test its efficiency by studying its performance for most well known single qubit noisy channels and for the generalised Pauli channel in arbitrary finite dimension.
• Continuous-time quantum error correction is a technique for protecting quantum information against decoherence, where both the decoherence and error correction processes are considered continuous in time. Given any [[$n,k,d$]] quantum stabilizer code, we formulate a class of protocols to implement CTQEC, involving weak coherent measurements and weak unitary corrections. Under this formalism, we show that the minimal required size of the ancillary system is $n-k+1$ qubits, and we propose one scheme that meets this minimal requirement. Furthermore, we compare our method with other known schemes, and show that a particular measure of performance described in this paper is better when using our method.
• We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms show an exponential speedup in both the number of training vectors $M$ and the feature space dimension $N$. We generalize the previous quantum algorithm for solving systems of linear equations [Phys. Rev. Lett. 103, 150502 (2009)] to efficiently implement a Hermitian chain product of $k$ normalized $N\times N$ Hermitian positive-semidefinite matrices with time complexity of $O(\log (N))$. Using this result, we perform linear as well as nonlinear Fisher discriminant analysis for dimensionality reduction over $M$ vectors, each in an $N$-dimensional feature space, in time $O(\log (MN)/\epsilon ^{3})$, where $\epsilon$ denotes the tolerance error. We also present a quantum discriminant analysis algorithm for data classification with time complexity $O(\log (MN)/\epsilon ^{3})$.
• We review moduli stabilization in type IIB string theory compactification with fluxes. We focus on the KKLT and Large Volume Scenario (LVS). We show that the predicted soft SUSY breaking terms in KKLT model are not phenomenological viable. In LVS, the following result for scalar mass, gaugino mass, and trilinear term is obtained: $m_0 =m_{1/2}= - A_0=m_{3/2}$, which may account for Higgs mass limit if $m_{3/2} \sim {\cal O}(1.5)$ TeV. However, in this case the relic abundance of the lightest neutralino can not be consistent with the measured limits. We also study the cosmological consequences of moduli stabilization in both models. In particular, the associated inflation models such as racetrack inflation and Kähler inflation are analyzed. Finally the problem of moduli destabilization and the effect of string moduli backreaction on the inflation models are discussed.
• In this paper we present a graph property with sensitivity $\Theta(\sqrt{n})$, where $n={v\choose2}$ is the number of variables, and generalize it to a $k$-uniform hypergraph property with sensitivity $\Theta(\sqrt{n})$, where $n={v\choose k}$ is again the number of variables. This yields the smallest sensitivity yet achieved for a $k$-uniform hypergraph property. We then show that, for even $k$, there is a $k$-uniform hypergraph property that demonstrates a quadratic gap between sensitivity and block sensitivity. This matches the previously known largest gap found by Rubinstein (1995) for a general Boolean function and Chakraborty (2005) for a cyclically invariant Boolean function, and is the first known example of such a gap for a graph or hypergraph property.
• AdS black holes with hyperbolic horizons provide strong-coupling descriptions of thermal CFT states on hyperboloids. The low-temperature limit of these systems is peculiar. In this note we show that, in addition to a large ground state degeneracy, these states also have an anomalously large holographic complexity, scaling logarithmically with the temperature. We speculate on whether this fact generalizes to other systems whose extreme infrared regime is formally controlled by Conformal Quantum Mechanics, such as various instances of near-extremal charged black holes.
• Neural networks are both computationally intensive and memory intensive, making them difficult to deploy on embedded systems with limited hardware resources. To address this limitation, We introduce a three stage pipeline: pruning, quantization and Huffman encoding, that work together to reduce the storage requirement of neural networks by 35x to 49x without affecting their accuracy. Our method first prunes the network by learning only the important connections. Next, we quantize the weights to enforce weight sharing, finally, we apply Huffman encoding. After the first two steps we retrain the network to fine tune the remaining connections and the quantized centroids. Pruning, reduces the number of connections by 9x to 13x; Quantization then reduces the number of bits that represent each connection from 32 to 5. On the ImageNet dataset, our method reduced the storage required by AlexNet by 35x from 240MB to 6.9MB, without loss of accuracy. Our method reduced the size of VGG16 by 49x from 552MB to 11.3MB, again with no loss of accuracy. This allows fitting the model into on-chip SRAM cache rather than off-chip DRAM memory, which has 180x less access energy.
• The lack of reliable data in developing countries is a major obstacle towards sustainable development, food security, and disaster relief. Poverty data, for example, is typically scarce, sparse in coverage, and labor-intensive to obtain. Remote sensing data such as high-resolution satellite imagery, on the other hand, is becoming increasingly available and inexpensive. Unfortunately, such data is highly unstructured and we lack techniques to automatically extract useful insights to inform policy decisions and help direct humanitarian efforts. We propose a novel machine learning approach to extract large-scale socioeconomic indicators from high-resolution satellite imagery. The main challenge is that training data is very scarce, making it difficult to apply modern techniques such as Convolutional Neural Networks (CNN). We therefore propose a transfer learning approach where nighttime light intensities are used as a data-rich proxy. We train a fully convolutional CNN model to predict nighttime lights from daytime imagery, simultaneously learning features that are useful for poverty prediction. The model learns filters identifying different terrains and man-made structures, including roads, buildings, and farmlands, without any supervision beyond nighttime lights. We demonstrate that these learned features are highly informative for poverty mapping, even approaching the predictive performance of survey data collected in the field.
• We introduce a solid material that is itself invisible, possessing identical electromagnetic properties as air (i.e. not a cloak) at a desired frequency. Such a material could provide improved mechanical stability, electrical conduction and heat dissipation to a system, without disturbing incident electromagnetic radiation. One immediate application would be towards perfect antenna radomes. Unlike cloaks, such a transparent and self-invisible material has yet to be demonstrated. Previous research has shown that a single sphere or cylinder coated with plasmonic or dielectric layers can have a dark-state with considerably suppressed scattering cross-section, due to the destructive interference between two resonances in one of its scattering channels. Nevertheless, a massive collection of these objects will have an accumulated and detectable disturbance to the original field distribution. Here we overcome this bottleneck by lining up the dark-state frequencies in different channels. Specifically, we derive analytically, verify numerically and demonstrate experimentally that deliberately designed corrugated metallic wires can have record-low scattering amplitudes, achieved by aligning the nodal frequencies of the first two scattering channels. This enables an arbitrary assembly of these wires to be omnidirectionally invisible and the effective constitutive parameters nearly identical to air. Measured transmission spectra at microwave frequencies reveal indistinguishable results for all the arrangements of the 3D-printed samples studied.
• In a variety of research areas, the bag of weighted vectors and the histogram are widely used descriptors for complex objects. Both can be expressed as discrete distributions. D2-clustering pursues the minimum total within-cluster variation for a set of discrete distributions subject to the Kantorovich-Wasserstein metric. D2-clustering has a severe scalability issue, the bottleneck being the computation of a centroid distribution that minimizes its sum of squared distances to the cluster members. In this paper, we develop three scalable optimization techniques, specifically, the subgradient descent method, ADMM, and modified Bregman ADMM, for computing the centroids of large clusters without compromising the objective function. The strengths and weaknesses of these techniques are examined through experiments; and scenarios for their respective usage are recommended. Moreover, we develop both serial and parallelized versions of the algorithms, collectively named the AD2-clustering. By experimenting with large-scale data, we demonstrate the computational efficiency of the new methods and investigate their convergence properties and numerical stability. The clustering results obtained on several datasets in different domains are highly competitive in comparison with some widely used methods' in the corresponding areas.
• By incorporating the nonempirical SCAN semilocal density functional [Sun, Ruzsinszky, and Perdew, Phys. Rev. Lett. 115, 036402 (2015)] in the underlying expression, we propose one hybrid (SCAN0) and three double-hybrid (SCAN0-DH, SCAN-QIDH, and SCAN0-2) density functionals, which are free of any empirical parameter. The SCAN-based hybrid and double-hybrid functionals consistently outperform their parent SCAN semilocal functional for a wide range of applications. The SCAN-based semilocal, hybrid, and double-hybrid functionals generally perform better than the corresponding PBE-based functionals. In addition, the SCAN0-2 and SCAN-QIDH double-hybrid functionals significantly reduce the qualitative failures of the SCAN semilocal functional, such as the self-interaction error and noncovalent interaction error, extending the applicability of the SCAN-based functionals to a very diverse range of systems.
• The recent experimental condensation of ultracold atoms in a triangular optical lattice with negative effective tunneling energies paves the way to study frustrated systems in a controlled environment. Here, we explore the critical behavior of the chiral phase transition in such a frustrated lattice in three dimensions. We represent the low-energy action of the lattice system as a two-component Bose gas corresponding to the two minima of the dispersion. The contact repulsion between the bosons separates into intra- and inter-component interactions, referred to as $V_{0}$ and $V_{12}$, respectively. We first employ a Huang-Yang-Luttinger approximation of the free energy. For $V_{12}/V_{0} = 2$, which corresponds to the bare interaction, this approach suggests a first order phase transition, at which both the U$(1)$ symmetry of condensation and the $\mathbb{Z}_2$ symmetry of the emergent chiral order is broken simultaneously. Furthermore, we perform a renormalization group calculation at one-loop order. We demonstrate that the coupling regime $0<V_{12}/V_0\leq1$ shares the critical behavior of the Heisenberg fixed point at $V_{12}/V_{0}=1$. For $V_{12}/V_0>1$ we show that $V_{0}$ flows to a negative value, while $V_{12}$ increases and remains positive. This results in a breakdown of the effective quartic field theory due to an cubic anisotropy, and again suggests a discontinuous phase transition.
• Kolmogorov's theory of turbulence predicts that only wavenumbers bellow some critical value, called Kolmogorov's dissipation number, are essential to describe the evolution of a three-dimensional fluid flow. A determining wavenumber, first introduced by Foias and Prodi for the 2D Navier-Stokes equations, is a mathematical analog of Kolmogorov's number. The purpose of this paper is to prove the existence of a time-dependent determining wavenumber for the 3D Navier-Stokes equations whose time average is bounded by Kolmogorov's dissipation wavenumber for all solutions on the global attractor whose intermittency is not extreme.
• DM-Ice is a program towards the first direct detection search for dark matter in the Southern Hemisphere with a 250 kg-scale NaI(Tl) crystal array. It will provide a definitive understanding of the modulation signal reported by DAMA by running an array at both Northern and Southern Hemisphere sites. A 17 kg predecessor, DM-Ice17, was deployed in December 2010 at a depth of 2457 m under the ice at the geographic South Pole and has concluded its 3.5 yr data run. An active R&D program is underway to investigate detectors with lower backgrounds and improved readout electronics; two crystals with 37 kg combined mass are currently operating at the Boulby Underground Laboratory. We report on the final analyses of the DM-Ice17 data and describe progress towards a 250 kg DM-Ice experiment.
• We present updated predictions for the cross-sections for pair production of squarks and gluinos at the LHC Run II. First of all, we update the calculations based on NLO+NLL partonic cross-sections by using the NNPDF3.0NLO global analysis. This study includes a full characterization of theoretical uncertainties from higher orders, PDFs and the strong coupling. Then, we explore the implications for this calculation of the recent NNPDF3.0 PDFs with NLO+NLL threshold resummation. We find that the shift in the results induced by the threshold-improved PDFs is within the total theory uncertainty band of the calculation based on NLO PDFs. However, we also observe that the central values of the cross-sections are modified both in a qualitative and a quantitative way, illustrating the relevance and impact of using threshold-improved PDFs together with resummed partonic cross-sections. The updated NLO+NLL cross-sections based on NNPDF3.0NLO are publicly available in the NLL-fast format, and should be an important ingredient for the interpretation of the searches for supersymmetric particles at Run II.
• We prove that a positive definite smooth four-manifold with $b_2^+ \geq 2$ and having either no 1-handles or no 3-handles cannot admit a symplectic structure.
• In this work, we explore an extension of Hilbert series techniques to count operators that include derivatives. For sufficiently low-derivative operators, we find an algorithm that gives the number of invariant operators, properly accounting for redundancies due to the equations of motion and integration by parts. Specifically, the technique can be applied whenever there is only one Lorentz invariant for a given partitioning of derivatives among the fields. At higher numbers of derivatives, equation of motion redundancies can be removed, but the increased number of Lorentz contractions spoils the subtraction of integration by parts redundancies. While restricted, this technique is sufficient to automatically generate the complete set of invariant operators of the Standard Model effective field theory for dimensions 6 and 7 (for arbitrary numbers of flavors). At dimension 8, the algorithm does not automatically generate the complete operator set; however, it suffices for all but five classes of operators. For these remaining classes, there is a well defined procedure to manually determine the number of invariants. Using these methods, we thereby derive the set of 535 dimension-8 $N_f = 1$ operators.
• Recent results in computing excited-state energies and meson-meson scattering phase shifts in lattice QCD are presented. A stochastic method of treating the low-lying modes of quark propagation that exploits Laplacian Heaviside quark-field smearing makes such studies possible now on large 32^3 x 256 and 48^3 x 128 lattices at near physical pion masses. Levels are identified using a variety of probe interpolating operators, which include both single-hadron and a large number of two-hadron operators.
• We demonstrate a velocity selection scheme that mitigates suppression of electromagnetically induced transparency (EIT) by Doppler shifts for low--high EIT probe--coupling wavelength ordering. An optical pumping beam counter-propagating with the EIT probe beam transfers atoms between hyperfine states in a velocity selective fashion. Measurement of the transmitted probe beam synchronous with chopping of the optical pumping beam enables a Doppler-free EIT signal to be detected. Transition frequencies between 5P$_{1/2}$ and $n$S$_{1/2}$ states for $n=$26, 27, and 28 in $^{39}$K are obtained via EIT spectroscopy in a heated vapor cell with a probe beam stabilized to the 4S$_{1/2}\rightarrow$5P$_{1/2}$ transition. Using previous high-resolution measurements of the 4S$_{1/2}\rightarrow$nS$_{1/2}$ transitions, we make a determination of the absolute frequency of the 4S$_{1/2}\rightarrow$5P$_{1/2}$ transition. Our measurement is shifted by 560 MHz from the currently accepted value with a two-fold improvement in uncertainty. These measurements will enable novel experiments with Rydberg-dressed ultracold Fermi gases composed of $^{40}$K atoms.
• It was recently proved that for $p>2m^{3}-4m^{2}+2m$ the constants of the Hardy--Littlewood inequality for $m$-linear forms on $\ell_{p}$-spaces are less than or equal to the best known estimates of respective constants of the Bohnenblust--Hille inequality. In this note we obtain upper bounds for opposite side, i.e., the constants when $2m\leq p\leq2m^{3}-4m^{2}+2m.$ For these values of $p$ our result improves previous estimates from 2014 of Araujo \textitet al. for all $m\geq3.$
• The fine-structure line of [OI] at 63micron is an important diagnostic tool in different fields of astrophysics. However, our knowledge of this line relies on observations with low spectral resolution, and the real contribution of each component (PDR, jet) in complex environment of star-forming regions (SFRs) is poorly understood. We investigate the contribution of jet and PDR emission, and of absorption to the [OI]63micron line towards the ultra-compact H\sc ii region G5.89--0.39 and study its far-IR line luminosity in different velocity regimes through [OI], [CII], CO, OH, and H2O. We mapped G5.89--0.39 in [OI] and in CO(16--15) with the GREAT receiver onboard SOFIA. We observed the central position of the source in the OH^2\Pi_3/2, J=5/2\toJ=3/2 and ^2\Pi_1/2, J=3/2\toJ=1/2 lines. These data were complemented with APEX CO(6-5) and CO(7-6) and HIFI maps and single-pointing observations in [CII], H2O, and HF. The [OI] spectra in G5.89--0.39 are severely contaminated by absorptions from the envelope and from different clouds along the line of sight. Emission is detected only at HV, clearly associated with the compact north-south outflows traced by extremely HV low-J CO. The mass-loss rate and energetics of derived from [OI] agree well with estimates from CO, suggesting that the molecular outflows in G5.89--0.39 are driven by the jet system seen in [OI]. The far-IR line luminosity of G5.89--0.39 is dominated by [OI] at HV; the second coolant in this velocity regime is CO, while [CII], OH and H2O are minor contributors to the cooling in the outflow. Our study shows the importance of spectroscopically resolved data of [OI]63micron for using this line as diagnostic of SFRs. While this was not possible until now, the GREAT receiver onboard SOFIA has recently opened the possibility of detailed studies of this line to investigate its potential for probing different environments.
• We prove the bounded packing property for any abelian subgroup of a group acting properly and cocompactly on a CAT(0) cube complex. A main ingredient of the proof is a cubical flat torus theorem. This ingredient is also used to show that central HNN extensions of maximal free-abelian subgroups of compact special groups are virtually special, and to produce various examples of groups that are not cocompactly cubulated.
• We lift the dynamical field of the $A_\infty$ superstring field theory to the large Hilbert space by introducing a trivial gauge invariance associated with the eta zero mode. We then provide a field redefinition which relates to the lifted field to the dynamical field of Berkovits' superstring field theory in the large Hilbert space. This generalizes the field redefinition in the small Hilbert space described in earlier works, and is useful for understanding the relation between the gauge symmetries of the theories.
• The structural and the magnetic properties of CeCu$_{6-x}$Ag$_x$ (0 $\leq$ $x$ $\leq$ 0.85) and CeCu$_{6-x}$Pd$_x$ (0 $\leq$ $x$ $\leq$ 0.4) have been studied using neutron diffraction, resonant ultrasound spectroscopy (RUS), heat capacity, x-ray diffraction measurements and first principles calculations. The structural and magnetic phase diagrams of CeCu$_{6-x}$Ag$_x$ and CeCu$_{6-x}$Pd$_x$ as a function of Ag/Pd composition are reported. The end member, CeCu$_6$, undergoes a structural phase transition from an orthorhombic ($Pnma$) to a monoclinic ($P2_1/c$) phase at 240 K. In CeCu$_{6-x}$Ag$_x$, the structural phase transition temperature (${T_{s}}$) decreases linearly with Ag concentration and extrapolates to zero at $x_{S}$ $\approx$ 0.1. The structural transition in CeCu$_{6-x}$Pd$_x$ remains unperturbed with Pd substitution within the range of our study. The lattice constant $b$ slightly decreases with Ag/Pd doping, whereas, $a$ and $c$ increase with an overall increase in the unit cell volume. Both systems, CeCu$_{6-x}$Ag$_x$ and CeCu$_{6-x}$Pd$_x$, exhibit a magnetic quantum critical point (QCP), at $x$ $\approx$ 0.2 and $x$ $\approx$ 0.05 respectively. Near the QCP, long range antiferromagnetic ordering takes place at an incommensurate wave vector ($\delta_1$ 0 $\delta_2$) where $\delta_1 \sim 0.62$, $\delta_2 \sim 0.25$, $x$ = 0.125 for CeCu$_{6-x}$Pd$_x$ and $\delta_1 \sim 0.64$, $\delta_2 \sim 0.3$, $x$ = 0.3 for CeCu$_{6-x}$Ag$_x$. The magnetic structure consists of an amplitude modulation of the Ce-moments which are aligned along the $c$-axis of the orthorhombic unit cell.
• Superconductivity results from a Bose condensate of Cooper-paired electrons with a macroscopic quantum wavefunction. Dramatic effects can occur when the region of the condensate is shaped and confined to the nanometer scale. Recent progress in nanostructured superconductors has revealed a route to topological superconductivity, with possible applications in quantum computing. However, challenges remain in controlling the shape and size of specific superconducting materials. Here, we report a new method to create nanostructured superconductors by partial crystallization of the half-Heusler material, YPtBi. Superconducting islands, with diameters in the range of 100 nm, were reproducibly created by local current annealing of disordered YPtBi in the tunneling junction of a scanning tunneling microscope (STM). We characterize the superconducting island properties by scanning tunneling spectroscopic measurements to determine the gap energy, critical temperature and field, coherence length, and vortex formations. These results show unique properties of a confined superconductor and demonstrate that this new method holds promise to create tailored superconductors for a wide variety of nanometer scale applications.
• Negative thermal expansion in ZrW2O8 was investigated using a flexibility analysis of ab-initio phonons. It was shown that no previously proposed mechanism adequately describes the atomic-scale drive towards negative thermal expansion in this system. Instead, it was found that NTE in ZrW2O8 is not driven by a single mechanism, but by many phonons that resemble vibrations of near-rigid WO4 units and Zr-O bonds at low frequency, with deformation of O-W-O and O-Zr-O bond angles steadily increasing with increasing NTE phonon frequency. It is asserted that this phenomenon is likely to provide a more accurate explanation for NTE in many complex systems not yet studied.
• The electric permittivities and magnetic permeabilities for a relativistic electron gas are calculated from quantum electrodynamics at finite temperature and density as functions of temperature, chemical potential, frequency, and wavevector. The polarization and the magnetization depend linearly on both electric and magnetic fields, and are the sum of a zero-temperature and zero-density vacuum part with a temperature- and chemical potential-dependent medium part. Analytic calculations lead to generalized expressions that depend on three scalar functions. In the nonrelativistic limit, results reproduce the Lindhard formula. In the relativistic case, and in the long wavelength limit, we obtain: i) for $\omega=0$, generalized susceptibilities that reduce to known nonrelativistic limits; ii) for $\omega \neq 0$, Drude-type responses at zero and at high temperatures. The latter implies that one may have both $\epsilon$ and $\mu$ simultaneously negative, a behavior characteristic of metamaterials. This unambiguously indicates that the relativistic electron plasma is one of nature's candidates for the realization of a negative index of refraction system. Moreover, Maxwell's equations in the medium yield the dispersion relation and the index of refraction of the electron plasma. Present results should be relevant for plasma physics, astrophysical observations, synchrotrons, and other environments with fast moving electrons.
• This paper investigates the achievable total degrees of freedom (DoF) of the MIMO multi-way relay channel that consists of K users, where each user is equipped with M antennas, and a decode-and-forward relay equipped with N antennas. In this channel, each user wants to convey K-1 private messages to the other users in addition to a common message to all of them. Due to the absence of direct links between the users, communication occurs through the relay in two phases; a multiple access channel phase (MAC) and a broadcast (BC) phase. We drive cut-set bounds on the total DoF of the network, and show that the network has DoF less than or equal to K min(N,M). Achievability of the upper bound is shown by using signal space alignment for network coding in the MAC phase, and zero-forcing precoding in the BC phase. We show that introducing the common messages besides the private messages leads to achieving higher total DoF than using the private messages only.
• A number of observational studies claim detection or non-detection of the extra line in X-ray spectra of various cosmic objects dominated by dark matter -- gravitationally interacting substance that constitutes the major fraction of non-relativistic matter in the Universe. In this review I summarize results of these studies and especially the status of the detection of new emission line at ~3.55 keV in spectra of nearby galaxies and galaxy clusters, overview possible interpretations of this line, including an intriguing connection with radiatively decaying dark matter, and show directions achievable with existing and upcoming X-ray cosmic missions.
• Let k be a finite extension of Q_p, let G be an absolutely simple split reductive group over k, and let K be a maximal unramified extension of k. To each point in the Bruhat-Tits building of G_K, Moy and Prasad have attached a filtration of G(K) by bounded subgroups. In this paper we give necessary and sufficient conditions for the dual of the first Moy-Prasad filtration quotient to contain stable vectors for the action of the reductive quotient. Our work extends earlier results by Reeder and Yu, who gave a classification in the case when p is sufficiently large. By passing to a finite unramified extension of k if necessary, we obtain new supercuspidal representations of G(k).
• We present an example of two countable $\omega$-categorical structures, one of which has a finite relational language, whose endomorphism monoids are isomorphic as abstract monoids, but not as topological monoids -- in other words, no isomorphism between these monoids is a homeomorphism. For the same two structures, the automorphism groups and polymorphism clones are isomorphic, but not topologically isomorphic. In particular, there exists a countable $\omega$-categorical structure in a finite relational language which can neither be reconstructed up to first-order bi-interpretations from its automorphism group, nor up to existential positive bi-interpretations from its endomorphism monoid, nor up to primitive positive bi-interpretations from its polymorphism clone.
• A new framework based on Boltzmann equation which is genuinely multidimensional and mesh-less is developed for solving Euler's equations. The idea is to use the method of moment of Boltzmann equation to operate in multidimensions using polar coordinates. The aim is to develop a framework which is genuinely multidimensional and can be implemented with different methodologies, no matter whether it is in finite difference, finite volume or finite element form. There is a considerable improvement in capturing shocks and other discontinuities. Also, since the method is multidimensional, the flow features are captured isotropically. The method is further extended to second order using 'Arc of Approach' concept. The framework is developed as a finite difference method (called as GINEUS) and is tested on the benchmark test cases. The results are compared against Kinetic Flux Vector Splitting Method.
• We study the optical characteristics of a photonic crystal (PhC) heterostructure cavity consisting of two-dimensional monolayer PhC, sandwiched between two identical passive multilayers. In the range of stopband of the multilayer, guided resonance of the sandwiched PhC are excited by the evanescent waves of the multilayer stack and the quality factor of these cavity-coupled guided resonances is about 10e6. The calculated field distribution facilitates the distinction between the cavity defect modes and the coupled guided resonances of the proposed design. The line shapes of the resonances are explained using a theoretical model. Significant decrease in the lasing threshold is observed for these resonant modes in comparison to the defect modes. These results will find use in designing compact PhC-based ultra-low threshold lasers and narrow band filters.
• A coding theorem and converse are proved for abstract channels with time structure that contain continuous-time continuous-valued channels and the result by Kadota and Wyner (1972) as special cases. As main contribution the coding theorem is proved for a significantly weaker condition on the channel output memory and without imposing extra measurability requirements to the channel. These improvements are achieved by introducing a suitable characterization of information rate capacity. It is shown that the previously used $\psi$-mixing condition is quite restrictive, in particular for the important class of Gaussian channels. In fact, it is proved that for Gaussian (e.g., fading or additive noise) channels the $\psi$-mixing condition is equivalent to finite output memory. Moreover, a weak converse is derived for all stationary channels with time structure. Intersymbol interference as well as input constraints are taken into account in a general and flexible way, including amplitude and average power constraints as special case. Formulated in rigorous mathematical terms complete, explicit, and transparent proofs are presented. As a side product a gap is closed in the proof of Kadota and Wyner regarding a lemma on the monotonicity of some sequence of normalized mutual informations. An operational perspective is taken and an abstract framework is established, which allows to treat discrete- and continuous-time channels with (possibly infinite) memory and arbitrary alphabets simultaneously in a unified way.
• A new experiment at Fermilab will measure the anomalous magnetic moment of the muon with a precision of 140 parts per billion (ppb). This measurement is motivated by the results of the Brookhaven E821 experiment that were first released more than a decade ago, which reached a precision of 540 ppb. As the corresponding Standard Model predictions have been refined, the experimental and theoretical values have persistently differed by about 3 standard deviations. If the Brookhaven result is confirmed at Fermilab with this improved precision, it will constitute definitive evidence for physics beyond the Standard Model. The experiment observes the muon spin precession frequency in flight in a well-calibrated magnetic field; the improvement in precision will require both 20 times as many recorded muon decay events as in E821 and a reduction by a factor of 3 in the systematic uncertainties. This paper describes the current experimental status as well as the plans for the upgraded magnet, detector and storage ring systems that are being prepared for the start of beam data collection in 2017.
• Emission from high-$z$ galaxies must unquestionably contribute to the Near-InfraRed Background (NIRB). However, this contribution has so far proven difficult to isolate even after subtracting resolved galaxies to deep levels. Remaining NIRB fluctuations are dominated by unresolved low-redshift galaxies on small angular scales, and by an unidentified component of unclear origin on large scales ($\approx 1000"$). In this paper, by analyzing mock maps generated from semi-numerical simulations and empirically determined $L_{\rm UV} - M_{\rm h}$ relations, we find that fluctuations associated with galaxies at $5 < z < 10$ amount to several percent of the unresolved NIRB flux. We investigate the properties of this component for different survey areas and limiting magnitudes. In all cases, we show that this signal can be efficiently, and most easily at small angular scales, isolated by cross-correlating the source-subtracted NIRB with Lyman Break Galaxies (LBGs) detected in the same field by \tt HST surveys. This result provides a fresh insight into the properties of reionization sources.
• We study mixing of the Dirac neutrinos in the residual symmetries approach. The key difference from the Majorana case is that the Dirac mass matrix may have larger symmetries: $G_\nu=\mathbf{Z}_{n}$ with $n\geq3$. The symmetry group relations have been generalized to the case of Dirac neutrinos. Using them we have found all new relations between mixing parameters and corresponding symmetry assignments which are in agreement with the present data. The viable relations exist only for the charged lepton residual symmetry $G_{\ell} = \mathbf{Z}_{2}$. The relations involve elements of the rows of the PMNS matrix and lead to precise predictions of the 2-3 mixing angle and certain ranges of the CP violation phase. For larger symmetries $G_{\ell}$, an agreement with data can be achieved if $\sim10\%$ corrections related to breaking of $G_{\ell}$ and $G_\nu$ are included.
• OPERA is a long-baseline experiment at the Gran Sasso laboratory (LNGS) designed to search for $\nu_\mu \rightarrow \nu_\tau$ oscillations in appearance mode. OPERA took data from 2008 to 2012 with the CNGS neutrino beam from CERN. The data analysis is ongoing, with the goal of establishing $\nu_\tau$ appearance with high significance and improving the sensitivity to the sterile neutrino search in the $\nu_\mu$ $\rightarrow$ $\nu_e$ appearance channel. Current results will be presented and perspectives discussed.
• In this paper we extend previous work of Galleas and the author to elliptic SOS models. We demonstrate that the dynamical reflection algebra can be exploited to obtain a functional equation characterizing the partition function of an elliptic SOS model with domain-wall boundaries and one reflecting end. Special attention is paid to the structure of the functional equation. Through this approach we find a novel multiple-integral formula for that partition function.
• We determine the asymptotic law for the fluctuations of the total number of critical points of random Gaussian spherical harmonics in the high degree limit. Our results have implications on the sophistication degree of an appropriate percolation process for modelling nodal domains of eigenfunctions on generic compact surfaces or billiards.
• We develop topological dynamics for the group of automorphisms of a monster model of any given theory. In particular, we find strong relationships between objects from topological dynamics (such as the generalized Bohr compactification introduced by Glasner) and various Galois groups of the theory in question, obtaining essentially new information about them, e.g. we present the closure of the identity in the Lascar Galois group of the theory as the quotient of a compact, Hausdorff group by a dense subgroup. We apply this to describe the complexity of bounded, invariant (not necessarily Borel) equivalence relations, obtaining comprehensive results, subsuming and extending the existing results and answering some open questions from earlier papers. We show that, in a countable theory, any such relation restricted to the set of realizations of a complete type over $\emptyset$ is type-definable if and only if it is smooth. Then we show a counterpart of this result for theories in an arbitrary (not necessarily countable) language, obtaining also new information involving relative definability of the relation in question. As a final conclusion we get the following trichotomy. Let $\mathfrak C$ be a monster model of a countable theory, $p \in S(\emptyset)$, and $E$ be a bounded, Borel (or even analytic) equivalence relation on $p(\mathfrak C)$. Then, exactly one of the following holds: a) $E$ is relatively definable (on $p(\mathfrak C)$), smooth, and has finitely many classes, b) $E$ is not relatively definable, but it is type-definable, smooth, and has $2^{\aleph_0}$ classes, c) $E$ is not type definable and not smooth, and has $2^{\aleph_0}$ classes. All the results which we obtain for bounded, invariant equivalence relations carry over to the case of bounded index, invariant subgroups of definable groups.
• We propose a method to "create" a new measurement output by exciting the system with a high-frequency oscillation. This new "virtual" measurement may be useful to facilitate the design of a suitable control law. The approach is especially interesting when the observability from the actual output degenerates at a steady-state regime of interest. The proposed method is based on second-order averaging and is illustrated by simulations on a simple third-order system.
• Coronal loops on the east limb of the Sun were observed by SUMER on SOHO for several days. Small flare-like brightenings are detected very frequently in the hot flare line Fe~\small XIX. We find that the relatively intense events are in good coincidence with the transient brightenings seen by Yohkoh/SXT. A statistical analysis shows that these brightenings have durations of 5-84 min and extensions along the slit of 2-67 Mm. The integrated energy observed in Fe~\small XIX for each event is in the range of $3\times10^{18}-5\times10^{23}$ ergs, and the estimated thermal energy ranges from $10^{26}-10^{29}$ ergs. Application of the statistical method proposed by Parnell \& Jupp (2000) yields a value of 1.5 to 1.8 for the index of a power law relation between the frequency of the events and the radiated energy in Fe~\small XIX, and a value of 1.7 to 1.8 for the index of the frequency distribution of the thermal energy in the energy range $>10^{27}$ ergs. We examine the possibility that these small brightenings give a big contribution to heating of the active region corona.
• We investigate the effect of time-dependent cyclic-adiabatic driving on the charge transport in quantum junction. We propose a nonequilibrium Greens function formalism to study statistics of the charge pumped (at zero bias) through the junction. The formulation is used to demonstrate charge pumping in a single electronic level coupled to two (electronic) reservoirs with time dependent couplings. Analytical expression for the average pumped current for a general cyclic driving is derived. It is found that for zero bias, for a certain class of driving, the Berry phase contributes only to the odd cumulants. To contrast, a quantum master equation formulation does not show Berry-phase effect at all.
• The amplitudes of the Evershed flow are measured using pairs of carefully selected FeI and FeII spectral lines located close in wavelength and registered simultaneously. A sunspot belonging to the NOAA 11582 group was scanned using the spectrograph of the German Vacuum Tower Telescope (Observatorio del Teide, Tenerife). Velocities were extracted from intensity profiles using the lambda-meter technique. The formation heights of the observed spectral lines were calculated using semi-empirical models of a bright and dark penumbral filament taking into account the sunspot location at the limb. Our objective is to compare azimuthally averaged amplitudes of the Evershed flow extracted from neutral and ion lines. We find measurable differences in the radial component of the flow. All five pairs of lines show the same tendency, with a few hundred m/s larger amplitude of the flow measured from FeI lines compared to FeII lines. This tendency is preserved at all photospheric heights and radial distances in the penumbra. We discuss the possible origin of this effect.
• The architecture of iso-orientation domains in the primary visual cortex of placental carnivores and primates apparently follows species invariant quantitative laws. Dynamical optimization models assuming that neurons coordinate their stimulus preferences throughout cortical circuits linking millions of cells specifically predict these invariants. This might indicate that V1's intrinsic connectome and its functional architecture adhere to a single optimization principle with high precision and robustness. To validate this hypothesis, it is critical to closely examine the quantitative predictions of alternative candidate theories. Random feedforward wiring within the retino-cortical pathway represents a conceptually appealing alternative to dynamical circuit optimization because random dimension-expanding projections are believed to generically exhibit computationally favorable properties for stimulus representations. Here, we ask whether the quantitative invariants of V1 architecture can be explained as a generic emergent property of random wiring. We generalize and examine the stochastic wiring model proposed by Ringach and coworkers, in which iso-orientation domains in the visual cortex arise through random feedforward connections between semi-regular mosaics of retinal ganglion cells (RGCs) and visual cortical neurons. We derive closed-form expressions for cortical receptive fields and domain layouts predicted by the model for perfectly hexagonal RGC mosaics [...] We conclude that V1 layout invariants are specific quantitative signatures of visual cortical optimization, which cannot be explained by generic random feedforward-wiring models. *See pdf for the full abstract.*
• In this paper, we propose an optimal active perception method for recognizing multimodal object categories. Multimodal categorization methods enable a robot to form several multimodal categories through interaction with daily objects autonomously. In most settings, the robot has to obtain all of the modality information when it attempts to recognize a new target object. However, even though a robot obtains visual information at a distance, it cannot obtain haptic and auditory information without taking action on the object. The robot has to determine its next action to obtain information about the object to recognize it. We propose an action selection method for multimodal object category recognition on the basis of the multimodal hierarchical Dirichlet process (MHDP) and information gain criterion. We also prove its optimality from the viewpoint of the Kullback--Leibler divergence between a final recognition state and a current recognition state. In addition, we show that the information gain has submodularity owing to the graphical model of the MHDP. On the basis of the submodular property of the information gain criterion, we propose sequential action selection methods, a greedy algorithm, and a lazy greedy algorithm. We conduct an experiment using an upper-torso humanoid robot and show that the method enables the robot to select actions actively and recognize target objects efficiently.

Travis Scholten Oct 02 2015 03:25 UTC

No worries with regards to the code - when it does get released, would you mind pinging me? You can find me on [GitHub](https://github.com/Travis-S).

Vlad Gheorghiu Sep 30 2015 03:19 UTC

I believe this work should mention the paper of Griffiths et al, "Atemporal diagrams for quantum circuits", PRA 73, 052309 (2006) http://journals.aps.org/pra/abstract/10.1103/PhysRevA.73.052309, arXiv:quant-ph/0507215 http://arxiv.org/abs/quant-ph/0507215. It is similar in flavour.

Nicola Pancotti Sep 23 2015 07:58 UTC

Hi Travis

Yes, that code is related to the work we did and that is my repo. However it is quite outdated. I used that repo for sharing the code with my collaborators. Now we are working for providing a human friendly version, commented and possibly optimized. If you would like to have a working

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Jianxin Chen Sep 23 2015 02:17 UTC

We noticed that our theorem 2 is the same as theorem 2 in http://journals.aps.org/pra/abstract/10.1103/PhysRevA.80.052306. We will revise our draft accordingly.

Chris Granade Sep 22 2015 19:15 UTC

Thank you for the kind comments, I'm glad that our paper, source code, and tutorial are useful!

Travis Scholten Sep 21 2015 17:08 UTC

Has anyone found some source code for the SGD referenced in this paper? I came across a [GitHub repository](https://github.com/nicaiola/thesisproject) from Nicola Pancotti (at least, I think that is his username, and the code seems to fit with the kind of work described in the paper!). I am not sure

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Travis Scholten Sep 21 2015 17:05 UTC

This was a really well-written paper! Am very glad to see this kind of work being done.

In addition, the openness about source code is refreshing. By explicitly relating the work to [QInfer](https://github.com/csferrie/python-qinfer), this paper makes it more easy to check the authors' work. Furthe

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Zoltán Zimborás Sep 18 2015 04:26 UTC

I can only quote Derrick Stolee: 'Terry Tao just dropped a bomb'. :)

Bill Plick Sep 16 2015 13:11 UTC

Ha!

For some background:

http://schroedingersrat.blogspot.fr/2014/07/letter-to-european-research-council.html