This paper surveys recent advances in the area of very large MIMO systems. With MIMO, we think systems that use antenna arrays with an order magnitude more elements than being built today, say a hundred antennas or more. Very entails unprecedented number simultaneously serving much smaller terminals. The disparity emerges as desirable operating condition and practical one well. terminals can be served is limited, not by antennas, but rather our inability to acquire channel-state information...

Abstract We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge neural networks. develop convolutional networks arbitrary manifolds $$\mathcal {M}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>M</mml:mi> </mml:math> using principal bundles with structure K maps between sections associated vector bundles. also discuss for homogeneous spaces {M}=G/K$$ <mml:mrow> <mml:mo>=</mml:mo> <mml:mi>G</mml:mi> <mml:mo>/</mml:mo>...

When formulated in twistor space, the D-instanton corrected hypermultiplet moduli space $ \mathcal{N} = {2} string vacua and Coulomb branch of rigid gauge theories on R3 × S 1 are strikingly similar and, to a large extent, dictated by consistency with wall-crossing. We elucidate this similarity showing that these two spaces related under general duality between, one hand, quaternion-Kähler manifolds quaternionic isometry other hyperkähler rotational isometry, equipped canonical...

The Mathieu twisted twining genera, i.e. the analogues of Norton's generalised Moonshine functions, are constructed for elliptic genus K3.It is shown that they satisfy expected consistency conditions, and their behaviour under modular transformations controlled by a 3-cocycle in H 3 (M24, U (1)), just as case holomorphic orbifolds.This suggests VOA may be underlying Moonshine.

We propose multiple-input multiple-output (MIMO) transmitter power allocation which takes dissipation in the amplifiers into account. derive equations of general problem with full channel state information (CSI), discuss its challenges, and supply solutions two special cases, namely for a single-output linear beamformer constraint, parallel MIMO channel. The proposed algorithms show substantial gains terms rate total consumed compared to previous art over wide range parameter settings, have...

This introduction to automorphic forms on adelic groups G(A) emphasises the role of representation theory. The exposition is driven by examples, and collects extends many results scattered throughout literature, in particular Langlands constant term formula for Eisenstein series as well Casselman–Shalika p-adic spherical Whittaker function. book also covers more advanced topics such Hecke algebras L-functions. Many these mathematical have natural interpretations string theory, so some basic...

We investigate quantum corrections to the hypermultiplet moduli space $ \mathcal{M} in Calabi-Yau compactifications of type II string theories, with particular emphasis on instanton effects from Euclidean NS5-branes. Based consistency D- and NS5-instanton corrections, we determine topology at fixed coupling, as previewed [1]. On IIB side, compute (p, k)-fivebrane instantons metric (specifically, correction complex contact structure its twistor \mathcal{Z} ) by applying S-duality D-instanton...

In this paper, Gaussian mixture modeling is applied to error concealment for block-based packet video. A model video data obtained offline and thereafter utilized online in order restore lost blocks from spatial temporal surrounding information. We propose estimators on closed form missing the case of varying available neighboring contexts. Our strategy increases peak signal-to-noise ratio compared previously proposed schemes. Examples improved subjective visual quality by means method are...

The hypermultiplet moduli space in Type IIA string theory compactified on a rigid Calabi-Yau threefold X , corresponding to the "universal hypermultiplet," is described at tree level by symmetric SU (2, 1)/(SU (2) × U (1)).To determine quantum corrections this metric, we posit that discrete subgroup of continuous isometry group 1), namely Picard modular 1; Z[i]), must remain unbroken exact metric -including all perturbative and non-perturbative corrections.This assumption expected be valid...

We consider four dimensional CHL models with sixteen spacetime supersymmetries obtained from orbifolds of type IIA superstring on K3 x T^2 by a Z_N symmetry acting (possibly) non-geometrically K3. show that most these (in particular, for geometric symmetries) are self-dual under weak-strong duality the heterotic axio-dilaton modulus S "Fricke involution" --> -1/NS. This is novel lies outside standard SL(2,Z)-symmetry parent theory, strings T^6. For this implies lattice purely electric...

We provide a physics derivation of Monstrous moonshine.We show that the McKay-Thompson series T g , ∈ M, can be interpreted as supersymmetric indices counting spacetime BPS-states in certain heterotic string models.The invariance groups these arise naturally T-duality and their genus zero property descends from behaviour models suitable decompactification limits.We also space forms module for Lie algebras m constructed by Borcherds Carnahan.We argue spontaneously broken gauge symmetries,...

Understanding the implications of SL(2, Z) S-duality for hypermultiplet moduli space type II string theories has led to much progress recently in uncovering D-instanton contributions.In this work, we suggest that extended duality group SL(3, Z), which includes both and Ehlers symmetry, may determine contributions D5 NS5-branes.We support claim by automorphizing perturbative corrections "extended universal hypermultiplet," a five-dimensional SO(3)\ R) subspace coupling, overall volume, Ramond...

We investigate multiple-input single-output channel capacity taking dissipation in the power amplifiers into account. consider case of a fixed with full state information (CSI) at both transmitter and receiver. The expression is given on closed form, we show that optimal solution antenna selection. An algorithm for finding minimum consumed any mutual further developed, power-mutual pair capacity-achieving. also ergodic Rayleigh fading CSI receiver no instantaneous transmitter. devise...

Motivated by string theory scattering amplitudes that are invariant under a discrete U-duality, we study Fourier coefficients of Eisenstein series on Kac-Moody groups.In particular, analyse the E 9 (R), 10 (R) and 11 corresponding to certain degenerate principal at values s = 3/2 5/2 were studied in [1].We show these have very simple as expected for their role supersymmetric contributions higher derivative couplings R 4 ∂ coming from 1/2-BPS 1/4-BPS instantons, respectively.This suggests...

We study the second quantized version of twisted twining genera generalized Mathieu moonshine, and verify that they give rise to Siegel modular forms with infinite product representations.Most these are expected have an interpretation as partition functions counting 1/4 BPS dyons in type II superstring theory on K3×T 2 or heterotic CHL-models.We show all forms, independently their possible physical interpretation, satisfy "S-duality" transformation a "wall-crossing formula".The latter...

A new method for multiple-input multiple-output (MIMO) detection with soft-output, the partial marginalization (PM) algorithm, was recently proposed. Advantages of are that it is straightforward to parallelize, and offers a fully predictable runtime. PM trades performance computational complexity via user-defined parameter. In limit high complexity, algorithm becomes MAP demodulator. The also works soft-input, but until now has been unclear how apply other modulation formats than binary...

By analyzing qualitative aspects of NS5-brane instanton corrections, we determine the topology hypermultiplet moduli space ${\mathcal{M}}_{\mathrm{H}}$ in Calabi-Yau compactifications type II string theories at fixed value dilaton and metric. Specifically, show that for fivebrane couplings to be well-defined, translations along intermediate Jacobian must induce nontrivial shifts Neveu-Schwarz axion which had thus far been overlooked. As a result, parametrizes fiber circle bundle, isomorphic...

In this paper we investigate in detail the correspondence between ${E}_{10}$ and Romans' massive deformation of type IIA supergravity. We analyze dynamics a nonlinear sigma model for spinning particle on coset space ${E}_{10}/K({E}_{10})$ show that it reproduces bosonic as well fermionic sector theory, within standard truncation. The mass parameter corresponds to generator outside realm generators entering usual $D=11$ analysis, is naturally included without any ${E}_{10}/K({E}_{10})$. Our...

In this paper we deal with spoofing detection in GNSS receivers. We derive the optimal genie detector when true positions are perfectly known, and observation errors Gaussian, as a benchmark for other detectors. The system model considers three dimensional positions, includes correlated errors. addition, propose several detectors that do not need any position knowledge, outperform recently proposed many interesting cases.

In this note, we expand on some technical issues raised in \cite{PPV} by the authors, as well providing a friendly introduction to and summary of our previous work. We construct set heterotic string compactifications 0+1 dimensions intimately related Monstrous moonshine module Frenkel, Lepowsky, Meurman (and orbifolds thereof). Using model, review physical interpretation genus zero property moonshine. Furthermore, show that space (second-quantized) BPS-states forms over Lie algebras...