Miracle-dz/UniFAR-FTUs huggingface dataset:
Molecular hydrogen in IllustrisTNG galaxies: carefully comparing signatures of environment with local CO and SFR data

We examine how the post-processed content of molecular hydrogen (H$_2$) in galaxies from the TNG100 cosmological, hydrodynamic simulation changes with environment at $z\! =\! 0$, assessing central/satellite status and host halo mass. We make close comparisons with the carbon monoxide (CO) emission survey xCOLD GASS where possible, having mock-observed TNG100 galaxies to match the survey's specifications. For a representative sample of host haloes across $10^{11}\! \lesssim\! M_{\rm 200c}/{\rm M}_{\odot}\! <\! 10^{14.6}$, TNG100 predicts that satellites with $m_*\! \geq\! 10^9\,{\rm M}_{\odot}$ should have a median deficit in their H$_2$ fractions of $\sim$0.6 dex relative to centrals of the same stellar mass. Once observational and group-finding uncertainties are accounted for, the signature of this deficit decreases to $\sim$0.2 dex. Remarkably, we calculate a deficit in xCOLD GASS satellites' H$_2$ content relative to centrals of 0.2--0.3 dex, in line with our prediction. We further show that TNG100 and SDSS data exhibit continuous declines in the average star formation rates of galaxies at fixed stellar mass in denser environments, in quantitative agreement with each other. By tracking satellites from their moment of infall in TNG100, we directly show that atomic hydrogen (HI) is depleted at fractionally higher rates than H$_2$ on average. Supporting this picture, we find that the H$_2$/HI mass ratios of satellites are elevated relative to centrals in xCOLD GASS. We provide additional predictions for the effect of environment on H$_2$ -- both absolute and relative to HI -- that can be tested with spectral stacking in future CO surveys.
Input-to-state stability of a scalar conservation law with nonlocal velocity

In this paper, we study input-to-state stability (ISS) of an equilibrium for a scalar conservation law with nonlocal velocity and measurement error arising in a highly re-entrant manufacturing system. By using a suitable Lyapunov function, we prove sufficient and necessary conditions on ISS. We propose a numerical discretization of the scalar conservation law with nonlocal velocity and measurement error. A suitable discrete Lyapunov function is analyzed to provide ISS of a discrete equilibrium for the proposed numerical approximation. Finally, we show computational results to validate the theoretical findings.
Physical Layer Security of Intelligent Reflective Surface Aided NOMA Networks

Intelligent reflective surface (IRS) technology is emerging as a promising performance enhancement technique for next-generation wireless networks. Hence, we investigate the physical layer security of the downlink in IRS-aided non-orthogonal multiple access networks in the presence of an eavesdropper, where an IRS is deployed for enhancing the quality by assisting the cell-edge user to communicate with the base station. To characterize the network's performance, the expected value of the new channel statistics is derived for the reflected links in the case of Nakagami-<inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> fading. Furthermore, the performance of the proposed network is evaluated both in terms of the secrecy outage probability (SOP) and the average secrecy capacity (ASC). The closed-form expressions of the SOP and the ASC are derived. We also study the impact of various network parameters on the overall performance of the network considered. To obtain further insights, the secrecy diversity orders and the high signal-to-noise-ratio (SNR) slopes are obtained. We finally show that: 1) the expectation of the channel gain in the reflected links is determined both by the number of IRS elements and by the Nakagami-<inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> fading parameters; 2) If the Nakagami-<inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> parameter is no less than 2, the SOP of both User 1 and User 2 becomes unity, when the number of IRS elements tends to infinity; 3) The secrecy diversity orders are affected both by the number of IRS elements and by the Nakagami-<inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> fading parameters, whereas the high-SNR slopes are not affected by these parameters. Our Monte-Carlo simulations perfectly demonstrate the analytical results.
Deep generative selection models of T and B cell receptor repertoires with soNNia

Significance The adaptive immune system relies on many types of B and T cells, whose functions are reflected in the distinct molecular features of their receptor sequences. Here, we introduce an inference framework, soNNia, which integrates interpretable knowledge-based models of immune receptor generation with flexible and powerful deep learning approaches to characterize sequence determinants of receptor function. Using soNNia, we characterize sequence-specific selection associated with receptors harvested from different cell types and tissues. We quantify synergetic interactions between the molecular features of the paired chains making up the receptor. Lastly, we develop a selection-based classifier to identify T cells specific to distinct pathogenic epitopes. Our approach provides a molecular understanding for how sequence determines the specific functionality of immune receptors. Subclasses of lymphocytes carry different functional roles to work together and produce an immune response and lasting immunity. Additionally to these functional roles, T and B cell lymphocytes rely on the diversity of their receptor chains to recognize different pathogens. The lymphocyte subclasses emerge from common ancestors generated with the same diversity of receptors during selection processes. Here, we leverage biophysical models of receptor generation with machine learning models of selection to identify specific sequence features characteristic of functional lymphocyte repertoires and subrepertoires. Specifically, using only repertoire-level sequence information, we classify CD4+ and CD8+ T cells, find correlations between receptor chains arising during selection, and identify T cell subsets that are targets of pathogenic epitopes. We also show examples of when simple linear classifiers do as well as more complex machine learning methods.
Detecting and Counting Small Subgraphs, and Evaluating a Parameterized Tutte Polynomial: Lower Bounds via Toroidal Grids and Cayley Graph Expanders

Given a graph property $\Phi$, we consider the problem $\mathtt{EdgeSub}(\Phi)$, where the input is a pair of a graph $G$ and a positive integer $k$, and the task is to decide whether $G$ contains a $k$-edge subgraph that satisfies $\Phi$. Specifically, we study the parameterized complexity of $\mathtt{EdgeSub}(\Phi)$ and of its counting problem $\#\mathtt{EdgeSub}(\Phi)$ with respect to both approximate and exact counting. We obtain a complete picture for minor-closed properties $\Phi$: the decision problem $\mathtt{EdgeSub}(\Phi)$ always admits an FPT algorithm and the counting problem $\#\mathtt{EdgeSub}(\Phi)$ always admits an FPTRAS. For exact counting, we present an exhaustive and explicit criterion on the property $\Phi$ which, if satisfied, yields fixed-parameter tractability and otherwise $\#\mathsf{W[1]}$-hardness. Additionally, most of our hardness results come with an almost tight conditional lower bound under the so-called Exponential Time Hypothesis, ruling out algorithms for $\#\mathtt{EdgeSub}(\Phi)$ that run in time $f(k)\cdot|G|^{o(k/\log k)}$ for any computable function $f$. As a main technical result, we gain a complete understanding of the coefficients of toroidal grids and selected Cayley graph expanders in the homomorphism basis of $\#\mathtt{EdgeSub}(\Phi)$. This allows us to establish hardness of exact counting using the Complexity Monotonicity framework due to Curticapean, Dell and Marx (STOC'17). Our methods can also be applied to a parameterized variant of the Tutte Polynomial $T^k_G$ of a graph $G$, to which many known combinatorial interpretations of values of the (classical) Tutte Polynomial can be extended. As an example, $T^k_G(2,1)$ corresponds to the number of $k$-forests in the graph $G$. Our techniques allow us to completely understand the parametrized complexity of computing the evaluation of $T^k_G$ at every pair of rational coordinates $(x,y)$.
Disentangling the AGN and Star formation Contributions to the Radio–X-Ray Emission of Radio-loud Quasars at 1 < Z < 2

We constrain the emission mechanisms responsible for the prodigious electromagnetic output generated by active galactic nuclei (AGNs) and their host galaxies with a novel state-of-the-art AGN radio-to-X-ray spectral energy distribution model fitting code (ARXSED). ARXSED combines multiple components to fit the spectral energy distributions (SEDs) of AGNs and their host galaxies. Emission components include radio structures such as lobes and jets, infrared emission from the AGN torus, visible-to-X-ray emission from the accretion disk, and radio-to-ultraviolet emission from the host galaxy. Applying ARXSED to the radio SEDs of 20 3CRR quasars at 1 < z < 2 verifies the need for more than a simple power law when compact radio structures are present. The nonthermal emission contributes 91%–57% of the observed-frame 1.25 mm to 850 μm flux, and this component must be accounted for when using these wavelengths to estimate star formation properties. We predict the presence of strong radio-linked X-ray emission in more than half the sample sources. ARXSED estimates median (and the associated first and third quartile ranges) BH mass of 2.91. 76.0×109M☉ , logarithm of Eddington ratio of −1.0−1.2−0.6 , and spin of 0.980. 940.99 for our sample. The inferred AGN torus and accretion disk parameters agree with those estimated from spectroscopic analyses of similar samples in the literature. We present the median intrinsic SED of the luminous radio-loud quasars at 1 < z ≲ 2; this SED represents a significant improvement in the way each component is modeled.
A Gleason–Kahane–Żelazko theorem for reproducing kernel Hilbert spaces

We establish the following Hilbert‐space analog of the Gleason–Kahane–Żelazko theorem. If H${\mathcal {H}}$ is a reproducing kernel Hilbert space with a normalized complete Pick kernel, and if Λ$\Lambda$ is a linear functional on H${\mathcal {H}}$ such that Λ(1)=1$\Lambda (1)=1$ and Λ(f)≠0$\Lambda (f)\ne 0$ for all cyclic functions f∈H$f\in {\mathcal {H}}$ , then Λ$\Lambda$ is multiplicative, in the sense that Λ(fg)=Λ(f)Λ(g)$\Lambda (fg)=\Lambda (f)\Lambda (g)$ for all f,g∈H$f,g\in {\mathcal {H}}$ such that fg∈H$fg\in {\mathcal {H}}$ . Moreover Λ$\Lambda$ is automatically continuous. We give examples to show that the theorem fails if the hypothesis of a complete Pick kernel is omitted. We also discuss conditions under which Λ$\Lambda$ has to be a point evaluation.
Apéry Limits: Experiments and Proofs

Abstract An important component of Apéry’s proof that is irrational involves representing as the limit of the quotient of two rational solutions to a three-term recurrence. We present various approaches to such Apéry limits and highlight connections to continued fractions as well as the famous theorems of Poincaré and Perron on difference equations. In the spirit of Jon Borwein, we advertise an experimental mathematics approach by first exploring in detail a simple but instructive motivating example. We conclude with various open problems.
The effects of a Robin boundary condition on thermal convection in a rotating spherical shell

Abstract Convection in a spherical shell is widely used to model fluid layers of planets and stars. The choice of thermal boundary conditions in such models is not always straightforward. To understand the implications of this choice, we report on the effects of the thermal boundary condition on thermal convection, in terms of instability onset, fully developed transport properties and flow structure. We impose a Robin boundary condition, enforcing linear coupling between the temperature anomaly and its radial derivative, with the Biot number ${{\textit {Bi}}}$ as a proportionality factor in non-dimensional form. Varying ${{\textit {Bi}}}$ allows us to transition from fixed temperature for ${{\textit {Bi}}}=+\infty$, to imposed heat flux for ${{\textit {Bi}}}=0$. We find that the onset of convection is only affected by ${{\textit {Bi}}}$ in the non-rotating case. Far from onset, considering an effective Rayleigh number and a generalized Nusselt number, we show that the Nusselt and Péclet numbers follow standard universal scaling laws, independent of ${{\textit {Bi}}}$ in all cases considered. However, for the non-rotating limit, the large-scale flow structure keeps the signature of the boundary condition with more vigorous large scales for smaller ${{\textit {Bi}}}$, even though the global heat transfer and kinetic energy are the same. For all practical purposes, the Robin condition can be safely replaced by a fixed flux when ${{\textit {Bi}}} \lesssim 0.03$ and by a fixed temperature for ${{\textit {Bi}}}\gtrsim 30$. For turbulent rapidly rotating convection, the thermal boundary condition does not seem to have any impact, once the effective numbers are considered and a reference temperature profile has been chosen.
The complexity of the Perfect Matching-Cut problem

Perfect Matching-Cut is the problem of deciding whether a graph has a perfect matching that is an edge cut. We show that this problem is $NP$-complete for planar graphs with maximum degree four, for planar graphs with girth five, for bipartite five-regular graphs, for graphs of diameter three and for bipartite graphs of diameter four. We show that there exist polynomial time algorithms for the following classes of graphs: claw-free, $P_5$-free, diameter two, bipartite with diameter three, quadrangulated and graphs with bounded tree-width.
Geometric conditions for saturating the data processing inequality

The data processing inequality (DPI) is a scalar inequality satisfied by distinguishability measures on density matrices. For some distinguishability measures, saturation of the scalar DPI implies an operator equation relating the arguments of the measure. These results are typically derived using functional analytic techniques. In a complementary approach, we use geometric techniques to derive a formula that gives an operator equation from DPI saturation for any distinguishability measure; moreover, for a broad class of distinguishability measures, the derived operator equation is sufficient to imply saturation as well. Our operator equation coincides with known results for the sandwiched Rényi relative entropies, and gives new results for α-z Rényi relative entropies and a family of of quantum f-divergences, which we compute explicitly.
Vertex Fault-Tolerant Geometric Spanners for Weighted Points

Given a set [Formula: see text] of [Formula: see text] points, a weight function [Formula: see text] to associate a non-negative weight to each point in [Formula: see text], a positive integer [Formula: see text], and a real number [Formula: see text], we present algorithms for computing a spanner network [Formula: see text] for the metric space [Formula: see text] induced by the weighted points in [Formula: see text]. The weighted distance function [Formula: see text] on the set [Formula: see text] of points is defined as follows: for any [Formula: see text], [Formula: see text] is equal to [Formula: see text] if [Formula: see text], otherwise, [Formula: see text] is [Formula: see text]. Here, [Formula: see text] is the Euclidean distance between [Formula: see text] and [Formula: see text] if points in [Formula: see text] are in [Formula: see text], otherwise, it is the geodesic (Euclidean) distance between [Formula: see text] and [Formula: see text]. The following are our results: (1) When the weighted points in [Formula: see text] are located in [Formula: see text], we compute a [Formula: see text]-vertex fault-tolerant [Formula: see text]-spanner network of size [Formula: see text]. (2) When the weighted points in [Formula: see text] are located in the relative interior of the free space of a polygonal domain [Formula: see text], we detail an algorithm to compute a [Formula: see text]-vertex fault-tolerant [Formula: see text]-spanner network with [Formula: see text] edges. Here, [Formula: see text] is the number of simple polygonal holes in [Formula: see text]. (3) When the weighted points in [Formula: see text] are located on a polyhedral terrain [Formula: see text], we propose an algorithm to compute a [Formula: see text]-vertex fault-tolerant [Formula: see text]-spanner network, and the number of edges in this network is [Formula: see text].
Eulerian ideals

Abstract Let G be a simple graph and , where is the homomorphism that sends an edge to the product of its vertices. The ideal is Cohen–Macaulay, one-dimensional and binomial. If G is bipartite, it is known that the Castelnuovo–Mumford regularity of is equal to the maximum cardinality of a set of edges having no more than half of the edges of any Eulerian subgraph of G. Here, with respect to the grevlex order associated to an ordering of the edge set of G, we describe a Gröbner basis for , and we characterize the standard monomials of the ideal in terms of even sets of vertices marked with a parity. Using these results, we give a combinatorial interpretation of the degree of , via the set of even sets of vertices of G; and we show that the Castelnuovo–Mumford regularity of , for any graph, is the maximum cardinality of a set of edges having no more than half of the edges of any even Eulerian subgraph of G or, equivalently, the maximum cardinality of a minimum fixed parity T-join.
Distributed Grid restoration based on graph theory

With the emergence of smart grids as the primary means of distribution across wide areas, the importance of improving its resilience to faults and mishaps is increasing. The reliability of a distribution system depends upon its tolerance to attacks and the efficiency of restoration after an attack occurs. This paper proposes a unique approach to the restoration of smart grids under attack by impostors or due to natural calamities via optimal islanding of the grid with primary generators and distributed generators(DGs) into sub-grids minimizing the amount of load shed which needs to be incurred and at the same time minimizing the number of switching operations via graph theory. The minimum load which needs to be shed is computed in the first stage followed by selecting the nodes whose load needs to be shed to achieve such a configuration and then finally deriving the sequence of switching operations required to achieve the configuration. The proposed method is tested against standard IEEE 37-bus and a 1069-bus grid system and the minimum load shed along with the sequencing steps to optimal configuration and time to achieve such a configuration are presented which demonstrates the effectiveness of the method when compared to the existing methods in the field. Moreover, the proposed algorithm can be easily modified to incorporate any other constraints which might arise due to any operational configuration of the grid.
Rare thermal bubbles at the many-body localization transition from the Fock space point of view

In this work we study the many-body localization (MBL) transition and relate it to the eigenstate structure in the Fock space. Besides the standard entanglement and multifractal probes, we introduce the radial probability distribution of eigenstate coefficients with respect to the Hamming distance in the Fock space from the wave function maximum and relate the cumulants of this distribution to the properties of the quasi-local integrals of motion in the MBL phase. We demonstrate non-self-averaging property of the many-body fractal dimension $D_q$ and directly relate it to the jump of $D_q$ as well as of the localization length of the integrals of motion at the MBL transition. We provide an example of the continuous many-body transition confirming the above relation via the self-averaging of $D_q$ in the whole range of parameters. Introducing a simple toy-model, which hosts ergodic thermal bubbles, we give analytical evidences both in standard probes and in terms of newly introduced radial probability distribution that the MBL transition in the Fock space is consistent with the avalanche mechanism for delocalization, i.e., the Kosterlitz-Thouless scenario. Thus, we show that the MBL transition can been seen as a transition between ergodic states to non-ergodic extended states and put the upper bound for the disorder scaling for the genuine Anderson localization transition with respect to the non-interacting case.
Edinburgh Research Explorer Understanding Pure Character-Based Neural Machine Translation: The Case of Translating Finnish into English

Recent work has shown that deeper character-based neural machine translation (NMT) models can outperform subword-based models. However, it is still unclear what makes deeper character-based models successful. In this paper, we conduct an investigation into pure character-based models in the case of translating Finnish into English, including exploring the ability to learn word senses and morphological inﬂections and the attention mechanism. We demonstrate that word-level information is distributed over the entire character sequence rather than over a single character, and characters at different positions play different roles in learning linguistic knowledge. In addition, character-based models need more layers to encode word senses which explains why only deeper models outperform subword-based models. The attention distribution pattern shows that separators attract a lot of attention and we explore a sparse word-level attention to enforce character hidden states to capture the full word-level information. Experimental results show that the word-level attention with a single head results in 1.2 BLEU points drop.
Generalization of Quasi-Newton Methods: Application to Robust Symmetric Multisecant Updates

Quasi-Newton techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other quasi-Newton schemes, such as BFGS, enforce symmetry but cannot satisfy more than one secant equation. We propose a new type of quasi-Newton symmetric update using several secant equations in a least-squares sense. Our approach generalizes and unifies the design of quasi-Newton updates and satisfies provable robustness guarantees.