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Inductive reasoning - the process of inferring general rules from a small number of observations - is a fundamental aspect of human intelligence. Recent works suggest that large language models (LLMs) can engage in inductive reasoning by sampling multiple hypotheses about the rules and selecting the one that best explains the observations. However, due to the IID sampling, semantically redundant hypotheses are frequently generated, leading to significant wastage of compute. In this paper, we 1) demonstrate that increasing the temperature to enhance the diversity is limited due to text degeneration issue, and 2) propose a novel method to improve the diversity while maintaining text quality. We first analyze the effect of increasing the temperature parameter, which is regarded as the LLM's diversity control, on IID hypotheses. Our analysis shows that as temperature rises, diversity and accuracy of hypotheses increase up to a certain point, but this trend saturates due to text degeneration. To generate hypotheses that are more semantically diverse and of higher quality, we propose a novel approach inspired by human inductive reasoning, which we call Mixture of Concepts (MoC). When applied to several inductive reasoning benchmarks, MoC demonstrated significant performance improvements compared to standard IID sampling and other approaches., Comment: 14 pages

In machine translation, the problem of ambiguously gendered input has been pointed out, where the gender of an entity is not available in the source sentence. To address this ambiguity issue, the task of controlled translation that takes the gender of the ambiguous entity as additional input have been proposed. However, most existing works have only considered a simplified setup of one target gender for input. In this paper, we tackle controlled translation in a more realistic setting of inputs with multiple entities and propose Gender-of-Entity (GoE) prompting method for LLMs. Our proposed method instructs the model with fine-grained entity-level gender information to translate with correct gender inflections. By utilizing four evaluation benchmarks, we investigate the controlled translation capability of LLMs in multiple dimensions and find that LLMs reach state-of-the-art performance in controlled translation. Furthermore, we discover an emergence of gender interference phenomenon when controlling the gender of multiple entities. Finally, we address the limitations of existing gender accuracy evaluation metrics and propose leveraging LLMs as an evaluator for gender inflection in machine translation., Comment: NAACL 2024 Main track long paper

Large Vision-Language Models (LVLMs) have demonstrated outstanding performance across various multimodal tasks. However, they suffer from a problem known as language prior, where responses are generated based solely on textual patterns while disregarding image information. Addressing the issue of language prior is crucial, as it can lead to undesirable biases or hallucinations when dealing with images that are out of training distribution. Despite its importance, current methods for accurately measuring language priors in LVLMs are poorly studied. Although existing benchmarks based on counterfactual or out-of-distribution images can partially be used to measure language priors, they fail to disentangle language priors from other confounding factors. To this end, we propose a new benchmark called VLind-Bench, which is the first benchmark specifically designed to measure the language priors, or blindness, of LVLMs. It not only includes tests on counterfactual images to assess language priors but also involves a series of tests to evaluate more basic capabilities such as commonsense knowledge, visual perception, and commonsense biases. For each instance in our benchmark, we ensure that all these basic tests are passed before evaluating the language priors, thereby minimizing the influence of other factors on the assessment. The evaluation and analysis of recent LVLMs in our benchmark reveal that almost all models exhibit a significant reliance on language priors, presenting a strong challenge in the field.

Quantum Annealing (QA)-accelerated MIMO detection is an emerging research approach in the context of NextG wireless networks. The opportunity is to enable large MIMO systems and thus improve wireless performance. The approach aims to leverage QA to expedite the computation required for theoretically optimal but computationally-demanding Maximum Likelihood detection to overcome the limitations of the currently deployed linear detectors. This paper presents X-ResQ, a QA-based MIMO detector system featuring fine-grained quantum task parallelism that is uniquely enabled by the Reverse Annealing (RA) protocol. Unlike prior designs, X-ResQ has many desirable system properties for a parallel QA detector and has effectively improved detection performance as more qubits are assigned. In our evaluations on a state-of-the-art quantum annealer, fully parallel X-ResQ achieves near-optimal throughput (over 10 bits/s/Hz) for $4\times6$ MIMO with 16-QAM using six levels of parallelism with 240 qubits and $220~\mu$s QA compute time, achieving 2.5--5$\times$ gains compared against other tested detectors. For more comprehensive evaluations, we implement and evaluate X-ResQ in the non-quantum digital setting. This non-quantum X-ResQ demonstration showcases the potential to realize ultra-large $1024\times1024$ MIMO, significantly outperforming other MIMO detectors, including the state-of-the-art RA detector classically implemented in the same way., Comment: 22 pages

Large antenna arrays can steer narrow beams towards a target area, and thus improve the communications capacity of wireless channels and the fidelity of radio sensing. Hardware that is capable of continuously-variable phase shifts is expensive, presenting scaling challenges. PIN diodes that apply only discrete phase shifts are promising and cost-effective; however, unlike continuous phase shifters, finding the best phase configuration across elements is an NP-hard optimization problem. Thus, the complexity of optimization becomes a new bottleneck for large-antenna arrays. To address this challenge, this paper suggests a procedure for converting the optimization objective function from a ratio of quadratic functions to a sequence of more easily solvable quadratic unconstrained binary optimization (QUBO) sub-problems. This conversion is an exact equivalence, and the resulting QUBO forms are standard input formats for various physics-inspired optimization methods. We demonstrate that a simulated annealing approach is very effective for solving these sub-problems, and we give performance metrics for several large array types optimized by this technique. Through numerical experiments, we report 3D beamforming performance for extra-large arrays with up to 10,000 elements.

We explore BPS strings in supergravity theories in six-dimensions and related Swampland Conjectures. We first propose a general modular ansatz for bootstrapping elliptic genera of 2d worldvolume theories on strings in the 6d theories. By employing mirror symmetry on F-theory examples, we explicitly compute the elliptic genera and validate our ansatz. We extend this approach to investigate BPS strings and their spectrum in non-geometric 6d theories which have no known F-theory constructions, and confirm the Swampland conjectures, including the Weak Gravity Conjecture, Distance Conjecture, and Emergent String Conjecture. We also discuss tensionless little strings that emerge near infinite-distance limits of strong gauge coupling in the moduli space of certain special theories., Comment: 72 pages, v2: minor corrections and references added

With the explosion of multimedia content, video moment retrieval (VMR), which aims to detect a video moment that matches a given text query from a video, has been studied intensively as a critical problem. However, the existing VMR framework evaluates video moment retrieval performance, assuming that a video is given, which may not reveal whether the models exhibit overconfidence in the falsely given video. In this paper, we propose the MVMR (Massive Videos Moment Retrieval for Faithfulness Evaluation) task that aims to retrieve video moments within a massive video set, including multiple distractors, to evaluate the faithfulness of VMR models. For this task, we suggest an automated massive video pool construction framework to categorize negative (distractors) and positive (false-negative) video sets using textual and visual semantic distance verification methods. We extend existing VMR datasets using these methods and newly construct three practical MVMR datasets. To solve the task, we further propose a strong informative sample-weighted learning method, CroCs, which employs two contrastive learning mechanisms: (1) weakly-supervised potential negative learning and (2) cross-directional hard-negative learning. Experimental results on the MVMR datasets reveal that existing VMR models are easily distracted by the misinformation (distractors), whereas our model shows significantly robust performance, demonstrating that CroCs is essential to distinguishing positive moments against distractors. Our code and datasets are publicly available: https://github.com/yny0506/Massive-Videos-Moment-Retrieval., Comment: accepted to CIKM 2024

We introduce anisotropic Banach spaces on Heisenberg nilmanifolds and study the resonance spectrum associated to partially hyperbolic automorphisms. In this work we describe an alternative proof of the spectrum which takes advantage of geometric-style anisotropic norms., Comment: Comments welcome

We propose two novel methods for computing the superconformal index of 5d superconformal field theories that cannot be described by conventional Lagrangian descriptions under mass deformations. The first approach involves the use of Higgs branch flows from UV Lagrangian theories, guided by transitions in 5-brane webs in Type IIB string theory. The second method employs the relationship between O$7^+$-plane and O$7^-$-plane with eight D7-branes, which applies to particular non-Lagrangian theories realized by brane configurations involving an O$7^+$-plane. As a concrete application of our method, we compute the superconformal indices for all known rank-1 non-Lagrangian theories, which we also use to identify flavor symmetries and their global forms at the conformal field theory (CFT) fixed points., Comment: 10 pages, 6 figures

Continuing the research initiated in \cite{Fr-Ki2}, we study the existence of solutions and their regularity for the cohomological equations $X u=f$ for locally Hamiltonian flows (determined by the vector field $X$) on a compact surface $M$ of genus $g\geq 1$. We move beyond the case studied so far by Forni in \cite{Fo1,Fo3}, when the flow is minimal over the entire surface and the function $f$ satisfies some Sobolev regularity conditions. We deal with the flow restricted to any its minimal component and any smooth function $f$ whenever the flow satisfies the Full Filtration Diophantine Condition (FFDC) (this is a full measure condition). The main goal of this article is to quantify optimal regularity of solutions. For this purpose we construct a family of invariant distributions $\mathfrak{F}_{\bar t}$, $\bar{t}\in\mathscr{TF}^*$ that play the roles of the Forni's invariant distributions introduced in \cite{Fo1,Fo3} by using the language of translation surfaces. The distributions $\mathfrak{F}_{\bar t}$ are global in nature (as emphasized in the title of the article), unlike the distributions $\mathfrak{d}^k_{\sigma,j}$, $(\sigma,k,j)\in\mathscr{TD}$ and $\mathfrak{C}^k_{\sigma,l}$, $(\sigma,k,l)\in\mathscr{TC}$ introduced in \cite{Fr-Ki2}, which are defined locally. All three families are used to determine the optimal regularity of the solutions for the cohomological equation, see Theorem 1.1 and 1.2. As a by-product, we also obtained, interesting in itself, a spectral result (Theorem 1.3) for the Kontsevich-Zorich cocycle acting on functional spaces arising naturally at the transition to the first-return map., Comment: The paper is closely related to the recent preprint: arXiv:2112.05939, arXiv:2112.13030 and arXiv:2305.16884

We study the cohomological equation $Xu=f$ for smooth locally Hamiltonian flows on compact surfaces. The main novelty of the proposed approach is that it is used to study the regularity of the solution $u$ when the flow has saddle loops, which has not been systematically studied before. Then we need to limit the flow to its minimum components. We show the existence and (optimal) regularity of solutions regarding the relations with the associated cohomological equations for interval exchange transformations (IETs). Our main theorems state that the regularity of solutions depends not only on the vanishing of the so-called Forni's distributions (cf.\ \cite{Fo1,Fo3}), but also on the vanishing of families of new invariant distributions (local obstructions) reflecting the behavior of $f$ around the saddles. Our main results provide some key ingredient for the complete solution to the regularity problem of solutions (in cohomological equations) for a.a.\ locally Hamiltonian flows (with or without saddle loops) to be shown in \cite{Fr-Ki3}. The main contribution of this article is to define the aforementioned new families of invariant distributions $\mathfrak{d}^k_{\sigma,j}$, $\mathfrak{C}^k_{\sigma,l}$ and analyze their effect on the regularity of $u$ and on the regularity of the associated cohomological equations for IETs. To prove this new phenomenon, we further develop local analysis of $f$ near degenerate singularities inspired by tools from \cite{Fr-Ki} and \cite{Fr-Ul2}. We develop new tools of handling functions whose higher derivatives have polynomial singularities over IETs., Comment: The paper is closely related to the recent preprint: arXiv:2112.05939, arXiv:2112.13030 and arXiv:2306.02340

Gender bias is a significant issue in machine translation, leading to ongoing research efforts in developing bias mitigation techniques. However, most works focus on debiasing bilingual models without much consideration for multilingual systems. In this paper, we specifically target the gender bias issue of multilingual machine translation models for unambiguous cases where there is a single correct translation, and propose a bias mitigation method based on a novel approach. Specifically, we propose Gender-Aware Contrastive Learning, GACL, which encodes contextual gender information into the representations of non-explicit gender words. Our method is target language-agnostic and is applicable to pre-trained multilingual machine translation models via fine-tuning. Through multilingual evaluation, we show that our approach improves gender accuracy by a wide margin without hampering translation performance. We also observe that incorporated gender information transfers and benefits other target languages regarding gender accuracy. Finally, we demonstrate that our method is applicable and beneficial to models of various sizes., Comment: Accepted to EMNLP 2023 Main Conference

Van der Waals (vdW) heterostructures, which are produced by the precise assemblies of varieties of two-dimensional (2D) materials, have demonstrated many novel properties and functionalities. Here we report a nano-plasmonic study of vdW heterostructures that were produced by depositing ordered molecular layers of pentacene on top of graphene. We find through nano-infrared (IR) imaging that surface plasmons formed due to the collective oscillations of Dirac fermions in graphene are highly sensitive to the adjacent pentacene layers. In particular, the plasmon wavelength declines systematically but nonlinearly with increasing pentacene thickness. Further analysis and density functional theory (DFT) calculations indicate that the observed peculiar thickness dependence is mainly due to the tunneling-type electron transfer from pentacene to graphene. Our work unveils a new method for tailoring graphene plasmons and deepens our understanding of the intriguing nano-optical phenomena due to interlayer couplings in novel vdW heterostructures., Comment: 21 pages

We report a nano-infrared (IR) imaging study of trilayer graphene (TLG) with both ABA (Bernal) and ABC (rhombohedral) stacking orders using the scattering-type scanning near-field optical microscope (s-SNOM). With s-SNOM operating in the mid-IR region, we mapped in real space the surface plasmon polaritons (SPPs) of ABA-TLG and ABC-TLG, which are tunable with electrical gating. Through quantitative modeling of the plasmonic imaging data, we found that the plasmon wavelength of ABA-TLG is significantly larger than that of ABC-TLG, resulting in a sizable impedance mismatch and hence a strong plasmon reflection at the ABA/ABC lateral junction. Further analysis indicates that the different plasmonic responses of the two types of TLG are directly linked to their electronic structures and carrier properties. Our work uncovers the physics behind the stacking-dependent plasmonic responses of TLG and sheds light on future applications of TLG and the ABA/ABC junctions in IR plasmonics and planar nano-optics., Comment: 11 pages

We propose blowup equations for 6d little string theories which generalize Nakajima-Yoshioka's blowup equations for the 4d/5d instanton partition functions on Omega background. We find that unlike the blowup equations for standard SQFTs, we need to sum over auxiliary magnetic fluxes on the blown-up $ \mathbb{P}^1$ for a non-dynamical 2-form gauge field which plays a role in canceling the mixed anomalies of the gauge symmetries. We demonstrate with explicit examples that the blowup equations, when combined with the modular properties, can be solved in order to determine the elliptic genera of little strings., Comment: 71 pages, 6 figures

Recently, diabetic retinopathy (DR) screening utilizing ultra-wide optical coherence tomography angiography (UW-OCTA) has been used in clinical practices to detect signs of early DR. However, developing a deep learning-based DR analysis system using UW-OCTA images is not trivial due to the difficulty of data collection and the absence of public datasets. By realistic constraints, a model trained on small datasets may obtain sub-par performance. Therefore, to help ophthalmologists be less confused about models' incorrect decisions, the models should be robust even in data scarcity settings. To address the above practical challenging, we present a comprehensive empirical study for DR analysis tasks, including lesion segmentation, image quality assessment, and DR grading. For each task, we introduce a robust training scheme by leveraging ensemble learning, data augmentation, and semi-supervised learning. Furthermore, we propose reliable pseudo labeling that excludes uncertain pseudo-labels based on the model's confidence scores to reduce the negative effect of noisy pseudo-labels. By exploiting the proposed approaches, we achieved 1st place in the Diabetic Retinopathy Analysis Challenge.

Convolutional Neural Networks (CNN) have been a good solution for understanding a vast image dataset. As the increased number of battery-equipped electric vehicles is flourishing globally, there has been much research on understanding which charge levels electric vehicle drivers would choose to charge their vehicles to get to their destination without any prevention. We implemented deep learning approaches to analyze the tabular datasets to understand their state of charge and which charge levels they would choose. In addition, we implemented the Image Generator for Tabular Dataset algorithm to utilize tabular datasets as image datasets to train convolutional neural networks. Also, we integrated other CNN architecture such as EfficientNet to prove that CNN is a great learner for reading information from images that were converted from the tabular dataset, and able to predict charge levels for battery-equipped electric vehicles. We also evaluated several optimization methods to enhance the learning rate of the models and examined further analysis on improving the model architecture.

We consider smooth locally Hamiltonian flows on compact surfaces of genus $g\geq 2$ to prove their deviation of Birkhoff integrals for smooth observables. Our work generalizes results of Forni and Bufetov which prove the existence of deviation spectrum of Birkhoff integrals for observables whose jets vanish at sufficiently high order around fixed points of the flow. They showed that ergodic integrals can display a power spectrum of behaviours with exactly $g$ positive exponents related to the positive Lyapunov exponents of the cocycle so-called Kontsevich-Zorich, a renormalization cocycle over the Teichm\"uller flow on a stratum of the moduli space of translation surfaces. Our paper extends the study of the spectrum of deviations of ergodic integrals beyond the case of observables whose jets vanish at sufficiently high order around fixed points. We prove the existence of some extra terms in deviation spectrum related to non-vanishing of the derivatives of observables at fixed points. The proof of this new phenomenon is based on tools developed in the recent work of the first author and Ulcigrai for locally Hamiltonian flows having only (simple) non-degenerate saddles. In full generality, due to the occurrence of (multiple) degenerate saddles, we introduce new methods of handling functions with polynomial singularities over a full measure set of IETs., Comment: The paper is closely related to the recent preprint arXiv:2112.05939

The layered metal phosphorous trisulfide FePS$_3$ is reported to be a Mott insulator at ambient conditions and to undergo structural and insulator-metal phase transitions under pressure. However, the character of the resulting metallic states has not been understood clearly so far. Here, we theoretically study the phase transitions of FePS$_3$ using first-principles methods based on density functional theory and embedded dynamical mean field theory. We find that the Mott transition in FePS$_3$ can be orbital-selective, with $t_{2g}$ states undergoing a correlation-induced insulator-to-metal transition while $e_g$ states remain gapped. We show that this orbital-selective Mott phase, which occurs only when non-hydrostatic pressure is used, is a bad metal (or non-Fermi liquid) with large fluctuating moments due to Hund's coupling. Further application of pressure increases the crystal-field splitting and converts the system to a conventional Fermi liquid with low-spin configurations dominant. Our results show that FePS$_3$ is a novel example of a system that realizes an orbital-selective Mott phase, allowing tuning between correlated and uncorrelated metallic properties in an accessible pressure range ($\leq$ 18 GPa)., Comment: 5 pages, 5 figures

We generalize Nakajima-Yoshioka's blowup formula to calculate the partition functions counting the spectrum of bound states to half-BPS Wilson loop operators in 5d (and 6d) supersymmetric field theories. The partition function in the presence of a Wilson loop operator on the $\Omega$-background is factorized when put on the blowup $\hat{\mathbb{C}}^2$ into two Wilson loop partition functions under the localization. This structure provides a set of blowup equations for Wilson loop operators. We explain how to formulate the blowup equations and solve them to compute the partition functions of Wilson loop operators. We test this idea by explicitly calculating the Wilson loop partition functions in various 5d/6d field theories and comparing them against known results and expected dualities., Comment: 69 pages, 3 figures, v2: published version

Overcoming the conventional trade-off between throughput and bit error rate (BER) performance, versus computational complexity is a long-term challenge for uplink Multiple-Input Multiple-Output (MIMO) detection in base station design for the cellular 5G New Radio roadmap, as well as in next generation wireless local area networks. In this work, we present ParaMax, a MIMO detector architecture that for the first time brings to bear physics-inspired parallel tempering algorithmic techniques [28, 50, 67] on this class of problems. ParaMax can achieve near optimal maximum-likelihood (ML) throughput performance in the Large MIMO regime, Massive MIMO systems where the base station has additional RF chains, to approach the number of base station antennas, in order to support even more parallel spatial streams. ParaMax is able to achieve a near ML-BER performance up to 160x160 and 80x80 Large MIMO for low-order modulations such as BPSK and QPSK, respectively, only requiring less than tens of processing elements. With respect to Massive MIMO systems, in 12x24 MIMO with 16-QAM at SNR 16 dB, ParaMax achieves 330 Mbits/s near-optimal system throughput with 4--8 processing elements per subcarrier, which is approximately 1.4x throughput than linear detector-based Massive MIMO systems., Comment: ACM MobiCom '21 (https://doi.org/10.1145/3447993.3448619)

Recently, we employed electronic polarization-resolved Raman spectroscopy to reveal the strongly correlated excitonic insulator (EI) nature of Ta2NiSe5, Volkov et al. [arXiv:2007.07344], and also showed that for Ta$_2$Ni(Se$_{1-x}$S$_x$)$_5$ alloys the critical excitonic fluctuations diminish with sulfur concentration x exposing a cooperating lattice instability that takes over for large x, Volkov et al. [arXiv:2104.07032]. Here we focus on the lattice dynamics of this EI family. We identify all Raman-active optical phonons of fully symmetric and ac-quadrupole-like symmetries and study their evolution with temperature and sulfur concentration. We demonstrate the change of selection rules at temperatures below the orthorhombic-to-monoclinic transition at Tc(x) that is related to the EI phase. We find that Tc(x) decrease monotonically from 328 K for Ta2NiSe5 to 120 K for Ta2NiS5 and that the magnitude of lattice distortion also decreases with the sulfur concentration x. For x < 0.7, the two lowest-frequency B2g phonon modes show strongly asymmetric lineshapes at high temperatures due to Fano interference with the broad excitonic continuum present in a semimetallic state. Within the framework of extended Fano model, we develop a quantitative description of the interacting exciton-phonon excitation lineshape, enabling us to derive the intrinsic phonon parameters and determine the exciton-phonon interaction strength, that affects the transition temperature Tc(x). We also observe signatures of the acoustic mode scattered assisted by the structural domain walls formed below Tc. Based on our results, we additionally present a consistent interpretation of the origin of oscillations observed in time-resolved pump-probe experiments.

We compute the partition function for 6d $\mathcal{N}=1$ $SO(2N)$ gauge theories compactified on a circle with $\mathbb{Z}_2$ outer automorphism twist. We perform the computation based on 5-brane webs with two O5-planes using topological vertex with two O5-planes. As representative examples, we consider 6d $SO(8)$ and $SU(3)$ gauge theories with $\mathbb{Z}_2$ twist. We confirm that these partition functions obtained from the topological vertex with O5-planes indeed agree with the elliptic genus computations., Comment: v1: 42 pages, 20 figures; v2: typos corrected; v3: typos corrected

We propose a systematic approach to computing the BPS spectra of any 5d/6d supersymmetric quantum field theory in Coulomb phases, which admits either gauge theory descriptions or geometric descriptions, based on the Nakajima-Yoshioka's blowup equations. We provide a significant generalization of the blowup equation approach in terms of both properly quantized magnetic fluxes on the blowup $\hat{\mathbb{C}}^2$ and the effective prepotential for 5d/6d field theories on the Omega background which is uniquely determined by the Chern-Simons couplings on their Coulomb branches. We employ our method to compute BPS spectra of all rank-1 and rank-2 5d Kaluza-Klein (KK) theories descending from 6d $\mathcal{N}=(1,0)$ superconformal field theories (SCFTs) compactified on a circle with/without twist. We also discuss various 5d SCFTs and KK theories of higher ranks, which include a few exotic cases such as new rank-1 and rank-2 5d SCFTs engineered with frozen singularity as well as the 5d $SU(3)_8$ gauge theory currently having neither a brane web nor a smooth shrinkable geometric description. The results serve as non-trivial checks for a large class of non-trivial dualities among 5d theories and also as independent evidences for the existence of certain exotic theories., Comment: 123 pages, 19 figures. v2 : References added, minor corrections

With unprecedented increases in traffic load in today's wireless networks, design challenges shift from the wireless network itself to the computational support behind the wireless network. In this vein, there is new interest in quantum-compute approaches because of their potential to substantially speed up processing, and so improve network throughput. However, quantum hardware that actually exists today is much more susceptible to computational errors than silicon-based hardware, due to the physical phenomena of decoherence and noise. This paper explores the boundary between the two types of computation---classical-quantum hybrid processing for optimization problems in wireless systems---envisioning how wireless can simultaneously leverage the benefit of both approaches. We explore the feasibility of a hybrid system with a real hardware prototype using one of the most advanced experimentally available techniques today, reverse quantum annealing. Preliminary results on a low-latency, large MIMO system envisioned in the 5G New Radio roadmap are encouraging, showing approximately 2--10X better performance in terms of processing time than prior published results., Comment: HotNets 2020: Nineteenth ACM Workshop on Hot Topics in Networks (https://doi.org/10.1145/3422604.3425924)

The main result of this paper is a construction of finitely additive measures for higher rank abelian actions on Heisenberg nilmanifolds. Under a full measure set of Diophantine conditions for the generators of the action, we construct \emph{Bufetov functionals} on rectangles on $(2g+1)$-dimensional Heisenberg manifolds. We prove that deviation of the ergodic integral of higher rank actions is described by the asymptotic of Bufetov functionals for a sufficiently smooth function. As a corollary, the distribution of normalized ergodic integrals which have variance 1, converges along certain subsequences to a non-degenerate compactly supported measure on the real line., Comment: 39 pages

The main results of this paper are to prove bounds for ergodic averages for nilflows on general higher step nilmanifolds. Under Diophantine condition on the frequency of a toral projection of the flow, we prove that almost all orbits become equidistributed at the polynomial speed. We analyze the exponent with the speed of decay which is determined by the number of steps and structure of general nilpotent Lie algebras. The main result follows from the technique over controlling scaling operators in irreducible representations and measure estimation on close return orbit on general nilmanifolds., Comment: 55 pages, 2 figues. arXiv admin note: text overlap with arXiv:1407.3640 by other authors

User demand for increasing amounts of wireless capacity continues to outpace supply, and so to meet this demand, significant progress has been made in new MIMO wireless physical layer techniques. Higher-performance systems now remain impractical largely only because their algorithms are extremely computationally demanding. For optimal performance, an amount of computation that increases at an exponential rate both with the number of users and with the data rate of each user is often required. The base station's computational capacity is thus becoming one of the key limiting factors on wireless capacity. QuAMax is the first large MIMO centralized radio access network design to address this issue by leveraging quantum annealing on the problem. We have implemented QuAMax on the 2,031 qubit D-Wave 2000Q quantum annealer, the state-of-the-art in the field. Our experimental results evaluate that implementation on real and synthetic MIMO channel traces, showing that 10~$\mu$s of compute time on the 2000Q can enable 48 user, 48 AP antenna BPSK communication at 20 dB SNR with a bit error rate of $10^{-6}$ and a 1,500 byte frame error rate of $10^{-4}$., Comment: https://dl.acm.org/doi/10.1145/3341302.3342072