Miracle-dz/UniFAR-FTUs huggingface dataset:
Topological properties of spaces admitting free group actions

In 1992, David Wright proved a remarkable theorem about which contractible open manifolds are covering spaces. He showed that if a one‐ended open manifold Mn has pro‐monomorphic fundamental group at infinity which is not pro‐trivial and is not stably ℤ, then M does not cover any manifold (except itself). In the non‐manifold case, Wright's method showed that when a one‐ended, simply connected, locally compact absolute neighborhood retract X with pro‐monomorphic fundamental group at infinity admits an action of ℤ by covering transformations, then the fundamental group at infinity of X is (up to pro‐isomorphism) an inverse sequence of finitely generated free groups. We improve upon this latter result, by showing that X must have a stable finitely generated free fundamental group at infinity. Simple examples show that a free group of any finite rank is possible.
Mittag-Leffler Waiting Time, Power Laws,Rarefaction, Continuous Time Random Walk, Diffusion Limit

We discuss some applications of the Mittag-Leffler function and related probability distributions in the theory of renewal processes and continuous time random walks. In particular we show the asymptotic (long time) equivalence of a generic power law waiting time to the Mittag-Leffler waiting time distribution via rescaling and respeeding the clock of time. By a second respeeding (by rescaling the spatial variable) we obtain the diffusion limit of the continuous time random walk under power law regimes in time and in space. Finally, we exhibit the time-fractional drift process as a diffusion limit of the fractional Poisson process and as a subordinator for space-time fractional diffusion.
Operator-GENERIC Formulation of Thermodynamics of Irreversible Processes

Metriplectic systems are state space formulations that have become well-known under the acronym GENERIC. In this work we present a GENERIC based state space formulation in an operator setting that encodes a weak-formulation of the field equations describing the dynamics of a homogeneous mixture of compressible heat-conducting Newtonian fluids consisting of reactive constituents. We discuss the mathematical model of the fluid mixture formulated in the framework of continuum thermodynamics. The fluid mixture is considered an open thermodynamic system that moves free of external body forces. As closure relations we use the linear constitutive equations of the phenomenological theory known as Thermodynamics of Irreversible Processes (TIP). The phenomenological coefficients of these linear constitutive equations satisfy the Onsager-Casimir reciprocal relations. We present the state space representation of the fluid mixture, formulated in the extended GENERIC framework for open systems, specified by a symmetric, mixture related dissipation bracket and a mixture related Poisson-bracket for which we prove the Jacobi-identity.
Phycocyanin improved alcohol-induced hepatorenal toxicity and behavior impairment in Wistar rats

Abstract The aim of this study was to investigate a potential preventive effect of phycocyanin extract from Spirulina platensis against ethanol- induced hepatorenal toxicity and cognitive behavior impairment in male Wistar rats. The animals were randomly and equally divided into four groups (six animals each): control group received saline solution, ethanol (EtOH) group was injected intraperitoneally with 1 ml/kg of ethanol solution 38% (w/v), phycocyanin groups were treated with 25 (PC1) or 50 (PC2) mg/kg phycocyanin extract followed by ethanol administration. All treatments were conducted for 14 successive days. Results revealed that ethanol induced oxidative stress in brain, liver, and kidney by increasing lipid peroxidation level and SOD and CAT activities. Serum biochemical perturbations were also observed in EtOH group, which was indicated by a significant elevation in ALT, AST, cholesterol, triglycerides, creatinine, and urea levels. Combined exposure to EtOH with phytocyanin contracted these biochemical alterations. Phycocyanin decreased also EtOH-induced anxiety and ameliorated exploratory behavior assessed by the elevated-plus maze and open field tests respectively.
The rate of convergence to stationarity for M/G/1 models with admission controls via coupling

Abstract We study the workload processes of two M/G/1 queueing systems with restricted capacity: in Model 1 any service requirement that would exceed a certain capacity threshold is truncated; in Model 2 new arrivals do not enter the system if they have to wait more than a fixed threshold time in line. For Model 1 we obtain several results concerning the rate of convergence to equilibrium. In particular, we derive uniform bounds for geometric ergodicity with respect to certain subclasses. For Model 2 geometric ergodicity follows from the finiteness of the moment-generating function of the service time distribution. We derive bounds for the convergence rates in special cases. The proofs use the coupling method.
Whitney regularity and Thom condition for families of non-isolated mixed singularities

We investigate the equisingularity question for $1$-parameter deformation families of mixed polynomial functions $f_t(\mathbf{z},\bar{\mathbf{z}})$ from the Newton polygon point of view. We show that if the members $f_t$ of the family satisfy a number of elementary conditions, which can be easily described in terms of the Newton polygon, then the corresponding family of mixed hypersurfaces $f_t^{-1}(0)$ is Whitney equisingular (and hence topologically equisingular) and satisfies the Thom condition.
The debt aversion survey module: An experimentally validated tool to measure individual debt aversion

We develop an experimentally validated, short and easy-to-use survey module for measuring individual debt aversion. To this end, we first estimate debt aversion on an individual level, using choice data from Meissner and Albrecht (2022). This data also contains responses to a large set of debt aversion survey items, consisting of existing items from the literature and novel items developed for this study. Out of these, we identify a survey module comprising two qualitative survey items to best predict debt aversion in the incentivized experiment.
Extended tensor products and generalization of the notion of entanglement

Motivated by the novel applications of the mathematical formalism of quantum theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the tensor product and entanglement. We also study the relation between conventional entanglement of complex qubits and our generalized entanglement. Our construction can also be used to describe entanglement in the framework of non-Archimedean physics. It is also possible to construct tensor products of non-Archimedean (e.g., p-adic) and complex Hilbert spaces.
Cross-Subject Emotion Recognition with Sparsely-Labeled Peripheral Physiological Data Using SHAP-Explained Tree Ensembles

—There are still many challenges of emotion recog- nition using physiological data despite the substantial progress made recently. In this paper, we attempted to address two major challenges. First, in order to deal with the sparsely-labeled physiological data, we ﬁrst decomposed the raw physiological data using signal spectrum analysis, based on which we extracted both complexity and energy features. Such a procedure helped reduce noise and improve feature extraction effectiveness. Second, in order to improve the explainability of the machine learning models in emotion recognition with physiological data, we proposed Light Gradient Boosting Machine (LightGBM) and SHapley Additive exPlanations (SHAP) for emotion prediction and model explanation, respectively. The LightGBM model out- performed the eXtreme Gradient Boosting (XGBoost) model on the public Database for Emotion Analysis using Physiological signals (DEAP) with f1-scores of 0.814, 0.823, and 0.860 for binary classiﬁcation of valence, arousal, and liking, respectively, with cross-subject validation using eight peripheral physiological signals. Furthermore, the SHAP model was able to identify the most important features in emotion recognition, and revealed the relationships between the predictor variables and the response variables in terms of their main effects and interaction effects. Therefore, the results of the proposed model not only had good performance using peripheral physiological data, but also gave more insights into the underlying mechanisms in recognizing emotions.
A reverse duality for the ASEP with open boundaries

We prove a duality between the asymmetric simple exclusion process (ASEP) with non-conservative open boundary conditions and an asymmetric exclusion process with particle-dependent hopping rates and conservative reflecting boundaries. This is a reverse duality in the sense that the duality function relates the measures of the dual processes rather than expectations. Specifically, for a certain parameter manifold of the boundary parameters of the open ASEP this duality expresses the time evolution of a family of shock product measures with N microscopic shocks in terms of the time evolution of N particles in the dual process. The reverse duality also elucidates some so far poorly understood properties of the stationary matrix product measures of the open ASEP given by finite-dimensional matrices.
Measuring Oscillations with a Million Atmospheric Neutrinos

After two decades of measurements, neutrino physics is now advancing into the precision era. Withthe long-baseline experiments designed to tackle current open questions, a new query arises: can atmospheric neutrino experiments also play a role? To that end, we analyze the expected sensitivity of current and near-future water(ice)-Cherenkov atmospheric neutrino experiments in the context of standard three-flavor neutrino oscillations. In this first in depth combined atmospheric neutrino analysis, we analyze the current shared systematic uncertainties arising from the common flux and neutrino-water interactions. We then implement the systematic uncertainties of each experiment in detail and develop the atmospheric neutrino simulations for Super-Kamiokande, with and without neutron-tagging capabilities, IceCube Upgrade, ORCA, and Hyper-Kamiokande detectors. We carefully review the synergies and features of these experiments to examine the potential of a joint analysis of these atmospheric neutrino data in resolving the $\theta_{23}$ octant at 99% confidence level, and determining the neutrino mass ordering above 5$\sigma$ by 2030. Additionally, we assess the capability to constrain $\theta_{13}$ and the CP -violating phase ($\delta_{CP}$) in the leptonic sector independently from reactor and accelerator neutrino data. A combination of the atmospheric neutrino measurements will enhance the sensitivity to a greater extent than the simple sum of individual experiment results reaching more than 3$\sigma$ for some values of $\delta_{CP}$ . These results will provide vital information for next-generation accelerator neutrino oscillation experiments such as DUNE and Hyper-Kamiokande.
Description of rank four PPT entangled states of two qutrits

It is known that some two qutrit entangled states of rank 4 with positive partial transpose (PPT) can be built from the unextendible product bases (UPB) [ Phys. Rev. Lett. 82, 5385 (1999) ]. We show that this fact is indeed universal, namely all such states can be constructed from UPB as conjectured recently by Leinaas, Myrheim and Sollid. We also classify the 5-dimensional subspaces of two qutrits which contain only finitely many product states (up to scalar multiple), and in particular those spanned by a UPB.
Gevrey regularity for the formally linearizable billiard of Treschev

Treschev made the remarkable discovery that there exists formal power series describing a billiard with locally linearizable dynamics. We show that if the frequency for the linear dynamics is Diophanine, the Treschev example is $(1+ \alpha)$-Gevrey for some $\alpha>0$. Our proof is based on an iterative scheme that further clarifies the structure and symmetries underlying the original Treschev construction. Hopefully, Our result sheds a light on the more important question of whether this example is convergent.
How to place an obstacle having a dihedral symmetry centered at a given point inside a disk so as to optimize the fundamental Dirichlet eigenvalue

A generic model for the shape optimization problems we consider in this paper is the optimization of the Dirichlet eigenvalues of the Laplace operator with a volume constraint. We deal with an obstacle placement problem which can be formulated as the following eigenvalue optimization problem: Fix two positive real numbers $r_1$ and $A$. We consider a disk $B\subset \mathbb{R}^2$ having radius $r_1$. We want to place an obstacle $P$ of area $A$ within $B$ so as to maximize or minimize the fundamental Dirichlet eigenvalue $\lambda_1$ for the Laplacian on $B\setminus P$. That is, we want to study the behaviour of the function $\rho \mapsto \lambda_1(B\setminus\rho(P))$, where $\rho$ runs over the set of all rigid motions of the plane fixing the center of mass for $P$ such that $\rho(P)\subset B$. In this paper, we consider this obstacle placement problem for the case where (i) the obstacle $P$ is invariant under the action of a dihedral group $\mathbb{D}_n, n >= 3,$ $n$ even, (ii) $P$ and $B$ have distinct centers, and (iii) the boundary $\partial P$ of $P$ satisfy certain monotonicity condition between each pair of consecutive axes of symmetry of $P$. The extremal configurations correspond to the cases where an axis of symmetry of $P$ coincide with an axis of symmetry of $B$. We also characterize the maximizing and the minimizing configurations in our main result, viz., Theorem 4.1. Further, we give many different generalizations of our result. At the end, we provide some numerical evidence to validate our main theorem for the case where the obstacle $P$ has $\mathbb{D}_4$ symmetry.
On the homology of the Harmonic Archipelago

We calculate the singular homology and Čech cohomology groups of the Harmonic Archipelago. As a corollary, we prove that this space is not homotopy equivalent to the Griffiths space. This is interesting in view of Eda’s proof that the first singular homology groups of these spaces are isomorphic.
High order steady-state diffusion approximation of the Erlang-C system

In this paper we introduce a new diffusion approximation for the steady-state customer count of the Erlang-C system. Unlike previous diffusion approximations, which use the steady-state distribution of a diffusion process with a constant diffusion coefficient, our approximation uses the steady-state distribution of a diffusion process with a \textit{state-dependent} diffusion coefficient. We show, both analytically and numerically, that our new approximation is an order of magnitude better than its counterpart. To obtain the analytical results, we use Stein's to show that a variant of the Wasserstein distance between the normalized customer count distribution and our approximation vanishes at a rate of $1/R$, where $R$ is the offered load to the system. In contrast, the previous approximation only achieved a rate of $1/R$. We hope our results motivate others to consider diffusion approximations with state-dependent diffusion coefficients.
Interplay of superconductivity and localization near a two-dimensional ferromagnetic quantum critical point

We study the superconducting instability of a two-dimensional disordered Fermi liquid weakly coupled to the soft fluctuations associated with proximity to an Ising-ferromagnetic quantum critical point. We derive interaction-induced corrections to the Usadel equation governing the superconducting gap function, and show that diffusion and localization effects drastically modify the interplay between fermionic incoherence and strong pairing interactions. In particular, we obtain the phase diagram, and demonstrate that: (i) there is an intermediate range of disorder strength where superconductivity is enhanced, eventually followed by a tendency towards the superconductor-insulator transition at stronger disorder; and (ii) diffusive particle-particle modes (so-called `Cooperons') acquire anomalous dynamical scaling $z=4$, indicating strong non-Fermi liquid behavior.
The Grushin hemisphere as a Ricci limit space with curvature $\ge 1$

The Grushin sphere is an almost-Riemannian manifold that degenerates along its equator. We construct a sequence of Riemannian metrics on a sphere $S^{m+n}$ with $Ric\ge 1$ such that its Gromov-Hausdorff limit is the $n$-dimensional Grushin hemisphere.
Global relaxation of bistable solutions for gradient systems in one unbounded spatial dimension

where spatial domain is the whole real line, state-parameter u is multidimensional, D denotes a fixed diffusion matrix, and the potential V is coercive at infinity. Bistable solutions, that is solutions close at both ends of space to stable homogeneous equilibria, are considered. For a solution of this kind, it is proved that, if the homogeneous equilibria approached at both ends belong to the same level set of the potential and if an appropriate (localized in space) energy remains bounded from below when time increases, then the solution approaches, when time approaches infinity, a pattern of stationary solutions homoclinic or heteroclinic to homogeneous equilibria. This result provides a step towards a complete description of the global behaviour of all bistable solutions that is pursued in a companion paper. Some consequences are derived, and applications to some examples are given.
Resonances in a single-lead reflection from a disordered medium: $\sigma$-model approach

Using the framework of supersymmetric non-linear $\sigma$-model we develop a general non-perturbative characterisation of universal features of the density $\rho(\Gamma)$ of the imaginary parts (``width'') for $S$-matrix poles (``resonances'') describing waves incident and reflected from a disordered medium via $M$-channel waveguide/lead. Explicit expressions for $\rho(\Gamma)$ are derived for several instances of systems with broken time-reversal invariance, in particular for quasi-1D and 3D media. In the case of perfectly coupled lead with a few channels ($M\sim 1$) the most salient features are tails $\rho(\Gamma)\sim \Gamma^{-1}$ for narrow resonances reflecting exponential localization and $\rho(\Gamma)\sim \Gamma^{-2}$ for broad resonances reflecting states located in the vicinity of the attached wire. For multimode quasi 1D wires with $M\gg 1$, an intermediate asymptotics $\rho(\Gamma)\sim \Gamma^{-3/2}$ is shown to emerge reflecting diffusive nature of decay into wide enough contacts.
Towards an Analytic Theory of Stochastic and Quantum Fields

We propose a method for the rigorous construction of physically relevant functional measures. In shaping it we get several conceptual insights, which can perhaps be summarized by the following statement: the renormalized interaction Lagrangian should be the generator of a flow on a space of asymptotically free cylinder functional measures with density given, in the case of Boson fields with polynomial self-interaction, by a generalized form of the Appell polynomials.
A Comprehensive Survey of Regression Based Loss Functions for Time Series Forecasting

Time Series Forecasting has been an active area of research due to its many applications ranging from network usage prediction, resource allocation, anomaly detection, and predictive maintenance. Numerous publications published in the last five years have proposed diverse sets of objective loss functions to address cases such as biased data, long-term forecasting, multicollinear features, etc. In this paper, we have summarized 14 well-known regression loss functions commonly used for time series forecasting and listed out the circumstances where their application can aid in faster and better model convergence. We have also demonstrated how certain categories of loss functions perform well across all data sets and can be considered as a baseline objective function in circumstances where the distribution of the data is unknown. Our code is available at GitHub: https://github.com/aryan-jadon/Regression-Loss-Functions-in-Time-Series-Forecasting-Tensorflow.
Spinorial classification of Spin(7) structures

We describe the different classes of $\mathrm{Spin(7)}$ structures in terms of spinorial equations. We relate them to the spinorial description of $\mathrm{G}_2$ structures in some geometrical situations. Our approach enables us to analyze invariant $\mathrm{Spin(7)}$ structures on quasi abelian Lie algebras.
Preserving Background Sound in Noise-Robust Voice Conversion Via Multi-Task Learning

Background sound is an informative form of art that is helpful in providing a more immersive experience in real-application voice conversion (VC) scenarios. However, prior research about VC, mainly focusing on clean voices, pay rare attention to VC with background sound. The critical problem for preserving background sound in VC is inevitable speech distortion by the neural separation model and the cascade mismatch between the source separation model and the VC model. In this paper, we propose an end-to-end framework via multitask learning which sequentially cascades a source separation (SS) module, a bottleneck feature extraction module and a VC module. Specifically, the source separation task explicitly considers critical phase information and limits the distortion caused by the imperfect separation process. The source separation task, the typical VC task and the unified task share a uniform reconstruction loss constrained by joint training to reduce the mismatch between the SS and VC modules. Experimental results demonstrate that our proposed framework significantly outperforms the baseline systems while achieving comparable quality and speaker similarity to the VC models trained with clean data.
Contrastive Learning enhanced Author-Style Headline Generation

Headline generation is a task of generating an appropriate headline for a given article, which can be further used for machine-aided writing or enhancing the click-through ratio. Current works only use the article itself in the generation, but have not taken the writing style of headlines into consideration. In this paper, we propose a novel Seq2Seq model called CLH3G (Contrastive Learning enhanced Historical Headlines based Headline Generation) which can use the historical headlines of the articles that the author wrote in the past to improve the headline generation of current articles. By taking historical headlines into account, we can integrate the stylistic features of the author into our model, and generate a headline not only appropriate for the article, but also consistent with the author’s style. In order to efficiently learn the stylistic features of the author, we further introduce a contrastive learning based auxiliary task for the encoder of our model. Besides, we propose two methods to use the learned stylistic features to guide both the pointer and the decoder during the generation. Experimental results show that historical headlines of the same user can improve the headline generation significantly, and both the contrastive learning module and the two style features fusion methods can further boost the performance.
Numerical Schubert calculus via the Littlewood-Richardson homotopy algorithm

We develop the Littlewood-Richardson homotopy algorithm, which uses numerical continuation to compute solutions to Schubert problems on Grassmannians and is based on the geometric Littlewood-Richardson rule. One key ingredient of this algorithm is our new optimal formulation of Schubert problems in local Stiefel coordinates as systems of equations. Our implementation can solve problem instances with tens of thousands of solutions.