Miracle-dz/UniFAR-FTUs huggingface dataset:
Colored Vertex Models and Iwahori Whittaker Functions

We give a recursive method for computing all values of a basis of Whittaker functions for unramified principal series invariant under an Iwahori or parahoric subgroup of a split reductive group $G$ over a nonarchimedean local field $F$. Structures in the proof have surprising analogies to features of certain solvable lattice models. In the case $G=\mathrm{GL}_r$ we show that there exist solvable lattice models whose partition functions give precisely all of these values. Here `solvable' means that the models have a family of Yang-Baxter equations which imply, among other things, that their partition functions satisfy the same recursions as those for Iwahori or parahoric Whittaker functions. The R-matrices for these Yang-Baxter equations come from a Drinfeld twist of the quantum group $U_q(\widehat{\mathfrak{gl}}(r|1))$, which we then connect to the standard intertwining operators on the unramified principal series. We use our results to connect Iwahori and parahoric Whittaker functions to variations of Macdonald polynomials.
Intrinsic nature of the giant spin Hall conductivity in Pt

More than a decade after the first theoretical and experimental studies of the spin Hall conductivity (SHC) of Pt, both its amplitude and dominant origin remain in dispute. Resolving these questions is of fundamental importance for advancing understanding of very strong spin-orbit effects in conducting systems and for maximizing the spin Hall effect (SHE) for energy-efficient spintronics applications. Here we report the incorporation of MgO scattering centers to controllably vary the degree of long-range crystalline ordering of Pt films and thus its band structure. We establish that the dominant mechanism for the giant SHC in Pt is the intrinsic SHE of the Pt bulk, whereas its amplitude is considerably underestimated by the available theoretical calculations. Our work also establishes a compelling new spin Hall material Pt0.6(MgO)0.4 that combines a giant spin Hall ratio (> 0.3), with a low resistivity, a strong Dzyaloshinskii-Moriya interaction, and good integration compatibility for spintronics technology.
Tensor networks for quantum causal histories

In this paper, we construct a tensor network representation of quantum causal histories, as a step towards directly representing states in quantum gravity via bulk tensor networks. Quantum causal histories are quantum extensions of causal sets in the sense that on each event in a causal set is assigned a Hilbert space of quantum states, and the local causal evolutions between events are modeled by completely positive and trace-preserving maps. Here we utilize the channel-state duality of completely positive and trace-preserving maps to transform the causal evolutions to bipartite entangled states. We construct the matrix product state for a single quantum causal history by projecting the obtained bipartite states onto the physical states on the events. We also construct the two dimensional tensor network states for entangled quantum causal histories in a restricted case with compatible causal orders. The possible holographic tensor networks are explored by mapping the quantum causal histories in a way analogous to the exact holographic mapping. The constructed tensor networks for quantum causal histories are exemplified by the non-unitary local time evolution moves in a quantum system on temporally varying discretizations, and these non-unitary evolution moves are shown to be necessary for defining a bulk causal structure and a quantum black hole. Finally, we comment on the limitations of the constructed tensor networks, and discuss some directions for further studies aiming at applications in quantum gravity.
5 Parallel Prism: A topology for pipelined implementations of convolutional neural networks using computational memory

In-memory computing is an emerging computing paradigm that could enable deeplearning inference at significantly higher energy efficiency and reduced latency. The essential idea is to map the synaptic weights corresponding to each layer to one or more computational memory (CM) cores. During inference, these cores perform the associated matrix-vector multiply operations in place with O(1) time complexity, thus obviating the need to move the synaptic weights to an additional processing unit. Moreover, this architecture could enable the execution of these networks in a highly pipelined fashion. However, a key challenge is to design an efficient communication fabric for the CM cores. Here, we present one such communication fabric based on a graph topology that is well suited for the widely successful convolutional neural networks (CNNs). We show that this communication fabric facilitates the pipelined execution of all state of-the-art CNNs by proving the existence of a homomorphism between one graph representation of these networks and the proposed graph topology. We then present a quantitative comparison with established communication topologies and show that our proposed topology achieves the lowest bandwidth requirements per communication channel. Finally, we present a concrete example of mapping ResNet-32 onto an array of CM cores.
Whither Programs as Specifications

Unifying theories distil common features of programming languages and design methods by means of algebraic operators and their laws. Several practical concerns --- e.g., improvement of a program, conformance of code with design, correctness with respect to specified requirements --- are subsumed by the beautiful notion that programs and designs are special forms of specification and their relationships are instances of logical implication between specifications. Mathematical development of this idea has been fruitful but limited to an impoverished notion of specification: trace properties. Some mathematically precise properties of programs, dubbed hyperproperties, refer to traces collectively. For example, confidentiality involves knowledge of possible traces. This article reports on both obvious and surprising results about lifting algebras of programming to hyperproperties, especially in connection with loops, and suggests directions for further research. The technical results are: a compositional semantics, at the hyper level, of imperative programs with loops, and proof that this semantics coincides with the direct image of a standard semantics, for subset closed hyperproperties.
Learning Transient Universe in Near-ultraviolet by Wide-angle Cameras

We perform a detailed analysis and simulations on the transient detection capability in the near-ultraviolet (NUV) band by focusing on some major local transient events. These events include the tidal disruption event due to a supermassive black hole, the shock breakout of a core-collapse supernova and the flare of a late-type star. Our simulations show that a set of small, wide-angle NUV cameras can allow us to detect and study numerous galactic and extragalactic transient events. Based on the analysis and simulations, here we propose a space-based NUV sky patrol mission by updating the proposal that was originally submitted to the Chinese Space Station mission in 2011. The mission proposed here is composed of a set of eight small wide-field NUV cameras each with a diameter of 20 cm. The total sky area simultaneously covered by the NUV cameras is as large as 3000 deg 2 . The survey cadence ranges from 30 to 300 s. The transient events are required to be detected by a dedicated onboard software in real time.
Attention-based Conditioning Methods for External Knowledge Integration

In this paper, we present a novel approach for incorporating external knowledge in Recurrent Neural Networks (RNNs). We propose the integration of lexicon features into the self-attention mechanism of RNN-based architectures. This form of conditioning on the attention distribution, enforces the contribution of the most salient words for the task at hand. We introduce three methods, namely attentional concatenation, feature-based gating and affine transformation. Experiments on six benchmark datasets show the effectiveness of our methods. Attentional feature-based gating yields consistent performance improvement across tasks. Our approach is implemented as a simple add-on module for RNN-based models with minimal computational overhead and can be adapted to any deep neural architecture.
Exhausting the background approach for bounding the heat transport in Rayleigh–Bénard convection

We revisit the optimal heat transport problem for Rayleigh–Bénard convection in which a rigorous upper bound on the Nusselt number, $Nu$ , is sought as a function of the Rayleigh number, $Ra$ . Concentrating on the two-dimensional problem with stress-free boundary conditions, we impose the time-averaged heat equation as a constraint for the bound using a novel two-dimensional background approach thereby complementing the ‘wall-to-wall’ approach of Hassanzadeh et al. (J. Fluid Mech., vol. 751, 2014, pp. 627–662). Imposing the same symmetry on the problem, we find correspondence with their maximal result for $Ra\leqslant Ra_{c}:=4468.8$ but, beyond that, the results from the two approaches diverge. The bound produced by the two-dimensional background field approaches that produced by the one-dimensional background field from below as the length of computational domain $L\rightarrow \infty$ . On lifting the imposed symmetry, the optimal two-dimensional temperature background field reverts to being one-dimensional, giving the best bound $Nu\leqslant 0.055Ra^{1/2}$ compared to $Nu\leqslant 0.026Ra^{1/2}$ in the non-slip case. We then show via an inductive bifurcation analysis that introducing two-dimensional temperature and velocity background fields (in an attempt to impose the time-averaged Boussinesq equations) is also unable to lower the bound. This then exhausts the background approach for the two-dimensional (and by extension three-dimensional) Rayleigh–Bénard problem with the bound remaining stubbornly $Ra^{1/2}$ while data seem more to scale like $Ra^{1/3}$ for large $Ra$ . Finally, we show that adding a velocity background field to the formulation of Wen et al. (Phys. Rev. E., vol. 92, 2015, 043012), which is able to use an extra vorticity constraint due to the stress-free condition to lower the bound to $Nu\leqslant O(Ra^{5/12})$ , also fails to further improve the bound.
Coin Theorems and the Fourier Expansion

In this note we compare two measures of the complexity of a class $\mathcal F$ of Boolean functions studied in (unconditional) pseudorandomness: $\mathcal F$'s ability to distinguish between biased and uniform coins (the coin problem), and the norms of the different levels of the Fourier expansion of functions in $\mathcal F$ (the Fourier growth). We show that for coins with low bias $\varepsilon = o(1/n)$, a function's distinguishing advantage in the coin problem is essentially equivalent to $\varepsilon$ times the sum of its level $1$ Fourier coefficients, which in particular shows that known level $1$ and total influence bounds for some classes of interest (such as constant-width read-once branching programs) in fact follow as a black-box from the corresponding coin theorems, thereby simplifying the proofs of some known results in the literature. For higher levels, it is well-known that Fourier growth bounds on all levels of the Fourier spectrum imply coin theorems, even for large $\varepsilon$, and we discuss here the possibility of a converse.
Graph Independence Testing

Identifying statistically significant dependency between variables is a key step in scientific discoveries. Many recent methods, such as distance and kernel tests, have been proposed for valid and consistent independence testing and can be applied to data in Euclidean and non-Euclidean spaces. However, in those works, $n$ pairs of points in $\mathcal{X} \times \mathcal{Y}$ are observed. Here, we consider the setting where a pair of $n \times n$ graphs are observed, and the corresponding adjacency matrices are treated as kernel matrices. Under a $\rho$-correlated stochastic block model, we demonstrate that a na\"ive test (permutation and Pearson's) for a conditional dependency graph model is invalid. Instead, we propose a block-permutation procedure. We prove that our procedure is valid and consistent -- even when the two graphs have different marginal distributions, are weighted or unweighted, and the latent vertex assignments are unknown -- and provide sufficient conditions for the tests to estimate $\rho$. Simulations corroborate these results on both binary and weighted graphs. Applying these tests to the whole-organism, single-cell-resolution structural connectomes of C. elegans, we identify strong statistical dependency between the chemical synapse connectome and the gap junction connectome.
Safe Reinforcement Learning Using Robust MPC

Reinforcement learning (RL) has recently impressed the world with stunning results in various applications. While the potential of RL is now well established, many critical aspects still need to be tackled, including safety and stability issues. These issues, while secondary for the RL community, are central to the control community that has been widely investigating them. Model predictive control (MPC) is one of the most successful control techniques because, among others, of its ability to provide such guarantees even for uncertain constrained systems. Since MPC is an optimization-based technique, optimality has also often been claimed. Unfortunately, the performance of MPC is highly dependent on the accuracy of the model used for predictions. In this article, we propose to combine RL and MPC in order to exploit the advantages of both, and therefore, obtain a controller that is optimal and safe. We illustrate the results with two numerical examples in simulations.
Loop-erased partitioning of a graph.

We consider a random partition of the vertex set of an arbitrary graph that can be efficiently sampled using loop-erased random walks stopped at a random independent exponential time of parameter $q>0$. The related random blocks tend to cluster nodes visited by the random walk---with generator minus the graph Laplacian---on time scale $1/q$, with $q$ being the tuning parameter. We explore the emerging macroscopic structure by analyzing 2-point correlations. To this aim, it is defined an interaction potential between pair of vertices, as the probability that they do not belong to the same block of the random partition.This interaction potential can be seen as an affinity measure for ``densely connected nodes'' and capture well-separated regions in network models presenting non-homogeneous landscapes. In this spirit, we compute the potential and its scaling limits on a complete graph and on a non-homogeneous weighted version with community structures. For the latter we show a phase-transition for detectability as a function of the tuning parameter and the edge weights.
Concentration inequalities in spaces of random configurations with positive Ricci curvatures

In this paper, we prove an Azuma-Hoeffding-type inequality in several classical models of random configurations, including the Erdős-Renyi random graph models $G(n,p)$ and $G(n,M)$, the random $d$-out(in)-regular directed graphs, and the space of random permutations. The main idea is using Ollivier's work on the Ricci curvature of Markov chairs on metric spaces. Here we give a cleaner form of such concentration inequality in graphs. Namely, we show that for any Lipschitz function $f$ on any graph (equipped with an ergodic random walk and thus an invariant distribution $\nu$) with Ricci curvature at least $\kappa>0$, we have \[\nu \left( |f-E_{\nu}f| \geq t \right) \leq 2\exp\left( -\frac{t^2\kappa}{7} \right). \]
Partially complex ranks for real projective varieties

Let $X(\mathbb {C})\subset \mathbb {P}^r(\mathbb {C})$ be an integral non-degenerate variety defined over $\mathbb {R}$. For any $q\in \mathbb {P}^r(\mathbb {R})$ we study the existence of $S\subset X(\mathbb {C})$ with small cardinality, invariant for the complex conjugation and with $q$ contained in the real linear space spanned by $S$. We discuss the advantages of these additive decompositions with respect to the $X(\mathbb {R})$-rank, i.e. the rank of $q$ with respect to $X(\mathbb {R})$. We describe the case of hypersurfaces and Veronese varieties.
Prediction of Research Topics Using Ensemble of Best Predictors from Similar Dataset

— Prediction of future research topics by using time series analysis either statistical or machine learning has been conducted previously by several researchers. Several methods have been proposed to combine the forecasting results into single forecast. These methods use fixed combination of individual forecast to get the final forecast result. In this paper, quite different approach is employed to select the forecasting methods, in which every point to forecast is calculated by using the best methods used by similar validation dataset. The dataset used in the experiment is time series derived from research report in Garuda, which is an online sites belongs to the Ministry of Education in Indonesia, over the past 20 years. The experimental result demonstrates that the proposed method may perform better compared to the fix combination of predictors. In addition, based on the prediction result, we can forecast emerging research topics for the next few years.
GSI: GPU-friendly Subgraph Isomorphism

Subgraph isomorphism is a well-known NP-hard problem that is widely used in many applications, such as social network analysis and querying over the knowledge graph. Due to the inherent hardness, its performance is often a bottleneck in various real-world applications. We address this by designing an efficient subgraph isomorphism algorithm leveraging features of GPU architecture, such as massive parallelism and memory hierarchy. Existing GPU-based solutions adopt two-step output scheme, performing the same join twice in order to write inter-mediate results concurrently. They also lack GPU architecture-aware optimizations that allow scaling to large graphs. In this paper, we propose a GPU-friendly subgraph isomorphism algorithm, GSI. Different from existing edge join-based GPU solutions, we propose a Prealloc-Combine strategy based on the vertex-oriented framework, which avoids joining-twice in existing solutions. Also, a GPU-friendly data structure (called PCSR) is proposed to represent an edge-labeled graph. Extensive experiments on both synthetic and real graphs show that GSI outperforms the state-of-the-art algorithms by up to several orders of magnitude and has good scalability with graph size scaling to hundreds of millions of edges.
DiCENet: Dimension-Wise Convolutions for Efficient Networks

We introduce a novel and generic convolutional unit, <monospace>DiCE</monospace> unit, that is built using dimension-wise convolutions and dimension-wise fusion. The dimension-wise convolutions apply light-weight convolutional filtering across each dimension of the input tensor while dimension-wise fusion efficiently combines these dimension-wise representations; allowing the <monospace>DiCE</monospace> unit to efficiently encode spatial and channel-wise information contained in the input tensor. The <monospace>DiCE</monospace> unit is simple and can be seamlessly integrated with any architecture to improve its efficiency and performance. Compared to depth-wise separable convolutions, the <monospace>DiCE</monospace> unit shows significant improvements across different architectures. When <monospace>DiCE</monospace> units are stacked to build the <monospace>DiCENet</monospace> model, we observe significant improvements over state-of-the-art models across various computer vision tasks including image classification, object detection, and semantic segmentation. On the ImageNet dataset, the <monospace>DiCENet</monospace> delivers 2-4 percent higher accuracy than state-of-the-art manually designed models (e.g., MobileNetv2 and ShuffleNetv2). Also, <monospace>DiCENet</monospace> generalizes better to tasks (e.g., object detection) that are often used in resource-constrained devices in comparison to state-of-the-art separable convolution-based efficient networks, including neural search-based methods (e.g., MobileNetv3 and MixNet).
Convolutional Bipartite Attractor Networks

In human perception and cognition, a fundamental operation that brains perform is interpretation: constructing coherent neural states from noisy, incomplete, and intrinsically ambiguous evidence. The problem of interpretation is well matched to an early and often overlooked architecture, the attractor network---a recurrent neural net that performs constraint satisfaction, imputation of missing features, and clean up of noisy data via energy minimization dynamics. We revisit attractor nets in light of modern deep learning methods and propose a convolutional bipartite architecture with a novel training loss, activation function, and connectivity constraints. We tackle larger problems than have been previously explored with attractor nets and demonstrate their potential for image completion and super-resolution. We argue that this architecture is better motivated than ever-deeper feedforward models and is a viable alternative to more costly sampling-based generative methods on a range of supervised and unsupervised tasks.
Les Mondes Darwiniens

1809 : naissance de Charles R. Darwin. 1859 : parution de L'Origine des especes. 2009 : cent cinquante ans plus tard, la theorie darwinienne de l'evolution reste le paradigme dominant de la biologie et de la paleontologie. Elle prouve sa fecondite et sa puissance explicative dans de tres nombreux domaines. Pourtant, dans cet ouvrage, pas question d'un fetichisme de Darwin, mais d'un examen attentif du domaine de validite epistemologique et experimental des idees du savant naturaliste. Ainsi, ce livre expose leurs multiples ramifications en sciences de la vie, en sciences humaines et en philosophie. a cette fin, cinquante auteurs explorent les grandes notions qui irriguent les sciences de l'evolution ; ainsi que de tres nombreux chantiers des savoirs biologiques contemporains ; puis considerent les tentatives d'exportation du mode de pensee darwinien a propos de problematiques autrefois hors de son champ d'action (ethique, psychologie, economie, etc.). Les questions du creationnisme et de l'enseignement viennent clore ce volume.
BER Performance of IM/DD FSO System with OOK using APD Receiver

In this paper, the performance of intensitymodulated with direct detection (IM/DD) free space optical (FSO) system using the on-off keying (OOK) and avalanche photodiode (APD) receiver is observed. The gamma-gamma model is used to describe the effect of atmospheric turbulence since it provides good agreement in the wide range of atmospheric conditions. In addition, the same FSO system with equal gain combining applied at the reception is analyzed. After theoretical derivation of the expression for the bit error rate (BER), the numerical integration with previously specified relative calculation error is performed. Numerical results are presented and confirmed by Monte Carlo simulations. The effects of the FSO link and receiver parameters on the BER performance are discussed. The results illustrate that the optimal APD gain in the minimum BER sense depends considerably on the link distance, atmospheric turbulence strength and receiver temperature. In addition, the value of this optimal gain is slightly different in the case of spatial diversity application compared with single channel reception.