Miracle-dz/UniFAR-FTUs huggingface dataset:
Unstable m= 1 modes of counter-rotating Keplerian discs

We study the linear m= 1 counter-rotating instability in a two-component, nearly Keplerian disc. Our goal is to understand these slow modes in discs orbiting massive black holes in galactic nuclei. They are of interest not only because they are of large spatial scale and can hence dominate observations but also because they can be growing modes that are readily excited by accretion events. Self-gravity being non-local, the eigenvalue problem results in a pair of coupled integral equations, which we derive for a two-component softened gravity disc. We solve this integral eigenvalue problem numerically for various values of mass fraction in the counter-rotating component. The eigenvalues are in general complex, being real only in the absence of the counter-rotating component, or imaginary when both components have identical surface density profiles. Our main results are as follows: (i) the pattern speed appears to be non-negative, with the growth (or damping) rate being larger for larger values of the pattern speed; (ii) for a given value of the pattern speed, the growth (or damping) rate increases as the mass in the counter-rotating component increases; (iii) the number of nodes of the eigenfunctions decreases with increasing pattern speed and growth rate. Observations of lopsided brightness distributions would then be dominated by modes with the least number of nodes, which also possess the largest pattern speeds and growth rates.
Towards Alzheimer's Disease Progression Assessment: A Review of Machine Learning Methods

: Alzheimer’s Disease (AD), as the most devastating neurodegenerative disease worldwide, has reached nearly 10 million new cases annually. Current technology provides unprecedented opportunities to study the progression and etiology of this disease with the advanced in imaging techniques. With the recent emergence of a society driven by big data and machine learning (ML), researchers have exerted considerable effort to summarize recent advances in ML-based AD diagnosis. Here, we outline some of the most prevalent and recent ML models for assessing the progression of AD and provide insights on the challenges, opportunities, and future directions that could be advantageous to future research in AD using ML.
Homotopy Algebras are Homotopy Algebras

We prove that strongly homotopy algebras (such as $A_\infty$, $C_\infty$, sh Lie, $B_\infty$, $G_\infty$,.) are homotopically invariant in the category of chain complexes. An important consequence is a rigorous proof that `strongly homotopy structures transfer over chain homotopy equivalences. '
$\mathcal{T,P}$-odd effects in the LuOH$^+$ cation

The LuOH$^+$ cation is a promising system to search for manifestations of time reversal and spatial parity violation effects. Such effects in LuOH$^+$ induced by the electron electric dipole moment $e$EDM and the scalar-pseudoscalar interaction of the nucleus with electrons, characterized by $k_s$ constant, in LuOH$^+$ are studied. The enhancement factors, polarization in the external electric field, hyperfine interaction, rovibrational structure are calculated. The study is required for the experiment preparation and extraction of the eEDM and ks values from experimental data.
Logits are predictive of network type

We show that it is possible to predict which deep network has generated a given logit vector with accuracy well above chance. We utilize a number of networks on a dataset, initialized with random weights or pretrained weights, as well as fine-tuned networks. A classifier is then trained on the logit vectors of the trained set of this dataset to map the logit vector to the network index that has generated it. The classifier is then evaluated on the test set of the dataset. Results are better with randomly initialized networks, but also generalize to pretrained networks as well as fine-tuned ones. Classification accuracy is higher using unnormalized logits than normalized ones. We find that there is little transfer when applying a classifier to the same networks but with different sets of weights. In addition to help better understand deep networks and the way they encode uncertainty, we anticipate our finding to be useful in some applications (e.g. tailoring an adversarial attack for a certain type of network). Code is available at https://github.com/aliborji/logits.
Operator-space Grothendieck inequalities for noncommutative $L_p$-spaces

We prove the operator space Grothendieck inequality for bilinear forms on subspaces of noncommutative $L_p$-spaces with $2<p<\infty$. One of our results states that given a map $u: E\to F^*$, where $E, F\subset L_p(M)$ ($2<p<\infty$, $M$ being a von Neumann algebra), $u$ is completely bounded iff $u$ factors through a direct sum of a $p$-column space and a $p$-row space. We also obtain several operator space versions of the classical little Grothendieck inequality for maps defined on a subspace of a noncommutative $L_p$-space ($2<p<\infty$) with values in a $q$-column space for every $q\in [p', p]$ ($p'$ being the index conjugate to $p$). These results are the $L_p$-space analogues of the recent works on the operator space Grothendieck theorems by Pisier and Shlyakhtenko. The key ingredient of our arguments is some Khintchine type inequalities for Shlyakhtenko's generalized circular systems. One of our main tools is a Haagerup type tensor norm, which turns out particularly fruitful when applied to subspaces of noncommutative $L_p$-spaces ($2<p<\infty$). In particular, we show that the norm dual to this tensor norm, when restricted to subspaces of noncommutative $L_p$-spaces, is equal to the factorization norm through a $p$-row space.
Quasi-local mass at null infinity in Bondi–Sachs coordinates

There are two important statements regarding the Trautman-Bondi mass at null infinity: one is the positivity, and the other is the Bondi mass loss formula, which are both global in nature. In this note, we compute the limit of the Wang-Yau quasi-local mass on unit spheres at null infinity of an asymptotically flat spacetime in the Bondi-Sachs coordinates. The quasi-local mass leads to a local description of the radiation that is purely gravitational at null infinity. In particular, the quasi-local mass is evaluated in terms of the news function of the Bondi-Sachs coordinates.
Asymptotical Cooperative Cruise Fault Tolerant Control for Multiple High-speed Trains with State Constraints

This paper investigates the asymptotical cooperative cruise fault tolerant control problem for multiple high-speed trains consisting of multiple carriages in the presence of actuator faults. A distributed state-fault observer utilizing the structural information of faults is designed to achieve asymptotical estimation of states and faults of each carriage. The observer does not rely on choice of control input, and thus it is separated from controller design. Based on the estimated values of states and faults, a distributed fault tolerance controller is designed to realize asymptotical cooperative cruise control of trains under the dual constraints of ensuring both position difference and velocity difference of adjacent trains in specified ranges throughout the whole process.
Cell Discovery in Millimeter Wave Systems: Physical Layer Implementations

Cell discovery is the procedure in which an user equipment (UE) in a cellular network finds a suitable base station (BS) and its physical layer cell identity, in order to establish a link-layer connection. When beamforming with antenna arrays is done at both transmitter and receiver, cell discovery in mm wave systems also involves finding the correct angle of arrival (AoA) - angle of departure (AoD) alignment between the UE and the detected BS. In this paper, we consider various existing and new schemes for cell discovery, present analytical studies on their detection probability and compare them in a common framework. In the first part, we study the conventional beam sweep technique and its variations, and present their physical layer training phase in detail. While the traditional beam sweep can not directly find the identity of the detected BS, we provide modifications in its training phase to enable the cell identity detection. In the second part of the paper, exploiting the sparseness of the mm wave channels and using an equivalent compressive sensing measurement model, we develop new cell discovery schemes with lesser overheads. One such design involves mutually unbiased bases (MUB) from quantum information theory. For the MUB based training scheme, we characterize the mutual coherence parameter of the resulting sensing matrix and establish its connection to the detection probability. We also present detailed simulation studies using experimentally driven mm wave channel simulators and show that our MUB based scheme gives superior performance compared to all the other schemes.
Polynomial bound for the partition rank vs the analytic rank of tensors

A tensor defined over a finite field $\mathbb{F}$ has low analytic rank if the distribution of its values differs significantly from the uniform distribution. An order $d$ tensor has partition rank 1 if it can be written as a product of two tensors of order less than $d$, and it has partition rank at most $k$ if it can be written as a sum of $k$ tensors of partition rank 1. In this paper, we prove that if the analytic rank of an order $d$ tensor is at most $r$, then its partition rank is at most $f(r,d,|\mathbb{F}|)$, where, for fixed $d$ and $\mathbb{F}$, $f$ is a polynomial in $r$. This is an improvement of a recent result of the author, where he obtained a tower-type bound. Prior to our work, the best known bound was an Ackermann-type function in $r$ and $d$, though it did not depend on $\mathbb{F}$. It follows from our results that a biased polynomial has low rank; there too we obtain a polynomial dependence improving the previously known Ackermann-type bound. A similar polynomial bound for the partition rank was obtained independently and simultaneously by Milicevic.
Benchmark of Bayesian Optimization and Metaheuristics for Control Engineering Tuning Problems with Crash Constraints

Controller tuning based on black-box optimization allows to automatically tune performance-critical parameters w.r. t. mostly arbitrary high-level closed-loop control objectives. However, a comprehensive benchmark of different black-box optimizers for control engineering problems has not yet been conducted. Therefore, in this contribution, 11 different versions of Bayesian optimization (BO) are compared with seven metaheuristics and other baselines on a set of ten deterministic simulative single-objective tuning problems in control. Results indicate that deterministic noise, low multimodality, and substantial areas with infeasible parametrizations (crash constraints) characterize control engineering tuning problems. Therefore, a flexible method to handle crash constraints with BO is presented. A resulting increase in sample efficiency is shown in comparison to standard BO. Furthermore, benchmark results indicate that pattern search (PS) performs best on a budget of 25 d objective function evaluations and a problem dimensionality d of d = 2. Bayesian adaptive direct search, a combination of BO and PS, is shown to be most sample efficient for 3<= d<= 5. Using these optimizers instead of random search increases controller performance by on average 6.6% and up to 16.1%.
Selection principles and the Minimal Tower problem

We study diagonalizations of covers using various selectionprinciples, where the covers are related to linearquasiorderings ( -covers). This includes: equivalences and nonequivalences,combinatorial characterizations, critical cardinalities andconstructions of special sets of reals.This study leads to a solution of a topological problem which wassuggested to the author by Scheepers (and stated in [15]) and is related to the Minimal Tower problem. We also introduce a variant of the notion of -cover,called -cover, and settle some problems for thisvariant which are still open in the case of -covers.This new variant introduces new (and tighter) topologicaland combinatorial lower bounds on the Minimal Tower problem.
Black-box Coreset Variational Inference

Recent advances in coreset methods have shown that a selection of representative datapoints can replace massive volumes of data for Bayesian inference, preserving the relevant statistical information and significantly accelerating subsequent downstream tasks. Existing variational coreset constructions rely on either selecting subsets of the observed datapoints, or jointly performing approximate inference and optimizing pseudodata in the observed space akin to inducing points methods in Gaussian Processes. So far, both approaches are limited by complexities in evaluating their objectives for general purpose models, and require generating samples from a typically intractable posterior over the coreset throughout inference and testing. In this work, we present a black-box variational inference framework for coresets that overcomes these constraints and enables principled application of variational coresets to intractable models, such as Bayesian neural networks. We apply our techniques to supervised learning problems, and compare them with existing approaches in the literature for data summarization and inference.
On finding all positive integers $a,b$ such that $b\pm a$ and $ab$ are palindromic

It is proven that the only integer solutions $(a,b)$ such that $a+b$ and $ab$ are palindromic are $(2,5\cdot 10^k-3)$, $(3,24)$ and $(9,9)$, and in a similar fashion, $b-a$ and $ab$ are only palindromic at $(a,b)=(3,147\cdot 10^{4(k+1)}+5247\sum_{i=0}^k10^{4i})$, $(3,161\,247\cdot 10^{4k+7}+5247\sum_{i=0}^k10^{4i+3}+387)$, $(3,147)$ and $(3,161\,247\,387)$ for $k=0,1,2,\cdots$. Note $a\le b$ without loss of generality.
Gradient-based iterative algorithms for solving Sylvester tensor equations and the associated tensor nearness problems

In this paper, an iterative algorithm is presented for solving Sylvester tensor equation $\mathscr{A}*_M\mathscr{X}+\mathscr{X}*_N\mathscr{C}=\mathscr{D}$, where $\mathscr{A}$, $\mathscr{C}$ and $\mathscr{D}$ are given tensors with appropriate sizes, and the symbol $*_N$ denotes the Einstein product. By this algorithm, the solvability of this tensor equation can be determined automatically, and the solution of which (when it is solvable) can be derived within finite iteration steps for any initial iteration tensors in the absence of roundoff errors. Particularly, the least F-norm solution of the aforementioned equation can be derived by choosing special initial iteration tensors. As application, we apply the proposed algorithm to the tensor nearness problem related to the Sylvester tensor equation mentioned above. It is proved that the solution to this problem can also be obtained within finite iteration steps by solving another Sylvester tensor equation. The performed numerical experiments show that the algorithm we propose here is promising.
Design of Trials with Composite Endpoints with the R Package CompAREdesign

Composite endpoints are widely used as primary endpoints in clinical trials. Designing trials with time-to-event endpoints can be particularly challenging because the proportional hazard assumption usually does not hold when using a composite endpoint, even when the premise remains true for their components. Consequently, the conventional formulae for sample size calculation do not longer apply. We present the R package CompAREdesign by means of which the key elements of trial designs, such as the sample size and effect sizes, can be computed based on the information on the composite endpoint components. CompAREdesign provides the functions to assess the sensitivity and robustness of design calculations to variations in initial values and assumptions. Furthermore, we describe other features of the package, such as functions for the design of trials with binary composite endpoints, and functions to simulate trials with composite endpoints under a wide range of scenarios.
Thermal Energy Budget of Electrons in the Inner Heliosphere: Parker Solar Probe Observations

We present an observational analysis of the electron thermal energy budget using data from Parker Solar Probe. We use the macroscopic moments, obtained from our fits to the measured electron distribution function, to evaluate the thermal energy budget based on the second moment of the Boltzmann equation. We separate contributions to the overall budget from reversible and irreversible processes. We find that an irreversible thermal energy source must be present in the inner heliosphere over the heliocentric distance range from 0.15 to 0.47 au. The divergence of the heat flux is positive at heliocentric distances below 0.33 au, while beyond 0.33 au, there is a measurable degradation of the heat flux. Expansion effects dominate the thermal energy budget below 0.3 au. Under our steady-state assumption, the free streaming of the electrons is not sufficient to explain the observed thermal energy density budget. We conjecture that the most likely driver for the required heating process is turbulence. Our results are consistent with the known nonadiabatic polytropic index of the electrons, which we measure as 1.18 in the explored range of heliocentric distances.
A Weakly-Supervised Streaming Multilingual Speech Model with Truly Zero-Shot Capability

Streaming automatic speech recognition (ASR) and speech translation (ST) tasks have extensively utilized neural transducers. In this paper, we present our endeavor to construct a Streaming Multilingual Speech Model (SM2), which employs a single neural transducer model for transcribing or translating multiple languages into target languages. SM2 is trained using weakly supervised data created by converting speech recognition transcriptions with a machine translation model. Leveraging 351 thousand hours of speech training data from 25 languages, SM2 achieves impressive ST performance. Furthermore, we demonstrate the truly zero-shot capability of SM2 when expanding to new target languages, generating high-quality zero-shot ST translation for {source-speech, target-text} pairs that were not seen during training.
Mirkovi\'c-Vilonen Polytopes and a quiver construction of crystal basis in type $A$

In the current paper, we give a quiver theoretical interpretation of Mirkovi\'c-Vilonen polytopes in type $A_n$. As a by-product, we give a new proof of the Anderson-Mirkovi\'c conjecture which describes the explicit forms of the actions of lowering Kashiwara operators on the set of Mirkovi\'c-Vilonen polytopes.
A theory of the invariants obtained from the moduli stacks of stable objects on a smooth polarized surface

Let $X$ be a smooth polarized algebraic surface over the compex number field. We discuss the invariants obtained from the moduli stacks of semistable sheaves of arbitrary ranks on $X$. For that purpose, we construct the virtual fundamental classes of some moduli stacks, and we show the transition formula of the integrals over the moduli stacks of the $\delta$-stable Bradlow pairs for the variation of the parameter $\delta$. Then, we study the relation among the invariants. In the case $p_g>0$, we show that the invariants are independent of the choice of a polarization of $X$. We also show that the invariants can be reduced to the invariants obtained from the moduli of abelian pairs and the Hilbert schemes. In the case $p_g=0$, we obtain the weak wall crossing formula and the weak intersection rounding formula, which describes the dependence of the invariants on the polarization.
The identification capacity and resolvability of channels with input cost constraint

Given a general channel, we first formulate the idetification capacity problem as well as the resolvability problem with input cost constraint in as the general form as possible, along with relevant fundamental theorems. Next, we establish some mild sufficient condition for the key lemma linking the identification capacity with the resolvability to hold for the continuous input alphabet case with input cost constraint. Under this mild condition, it is shown that we can reach the {\em continuous}-input fundamental theorem of the same form as that for the fundamental theorem with {\em finite} input alphabet. Finally, as important examples of this continuous-input fundamental theorem, we show that the identification capacity as well as the resolvability coincides with the channel capacity for stationary additive white (and also non-white) Gaussian noise channels.
Accelerating Cosmologies in the Einstein-Gauss-Bonnet Theory with Dilaton

We study cosmological solutions in the low-energy effective heterotic string theory, which is the Einstein gravity with Gauss-Bonnet term and the dilaton. We show that the field equations are cast into an autonomous system for flat internal and external spaces, and derive all the fixed points in the system. We also examine the time evolution of the solutions and whether the solutions can give (transient) accelerated expansion of our four-dimensional space in the Einstein frame.
The Benefits of Model-Based Generalization in Reinforcement Learning

Model-Based Reinforcement Learning (RL) is widely believed to have the potential to improve sample efficiency by allowing an agent to synthesize large amounts of imagined experience. Experience Replay (ER) can be considered a simple kind of model, which has proved effective at improving the stability and efficiency of deep RL. In principle, a learned parametric model could improve on ER by generalizing from real experience to augment the dataset with additional plausible experience. However, given that learned value functions can also generalize, it is not immediately obvious why model generalization should be better. Here, we provide theoretical and empirical insight into when, and how, we can expect data generated by a learned model to be useful. First, we provide a simple theorem motivating how learning a model as an intermediate step can narrow down the set of possible value functions more than learning a value function directly from data using the Bellman equation. Second, we provide an illustrative example showing empirically how a similar effect occurs in a more concrete setting with neural network function approximation. Finally, we provide extensive experiments showing the benefit of model-based learning for online RL in environments with combinatorial complexity, but factored structure that allows a learned model to generalize. In these experiments, we take care to control for other factors in order to isolate, insofar as possible, the benefit of using experience generated by a learned model relative to ER alone.
DUVET: Spatially Resolved Observations of Star Formation Regulation via Galactic Outflows in a Starbursting Disk Galaxy

We compare 500 pc scale, resolved observations of ionized and molecular gas for the z ∼ 0.02 starbursting disk galaxy IRAS08339+6517, using measurements from KCWI and NOEMA. We explore the relationship of the star-formation-driven ionized gas outflows with colocated galaxy properties. We find a roughly linear relationship between the outflow mass flux ( Σ̇out ) and star formation rate surface density (ΣSFR), Σ̇out∝ΣSFR1. 06±0.10 , and a strong correlation between Σ̇out and the gas depletion time, such that Σ̇out∝tdep−1.1±0.06 . Moreover, we find these outflows are so-called breakout outflows, according to the relationship between the gas fraction and disk kinematics. Assuming that ionized outflow mass scales with total outflow mass, our observations suggest that the regions of highest ΣSFR in IRAS08 are removing more gas via the outflow than through the conversion of gas into stars. Our results are consistent with a picture in which the outflow limits the ability of a region of a disk to maintain short depletion times. Our results underline the need for resolved observations of outflows in more galaxies.