Miracle-dz/UniFAR-FTUs huggingface dataset:
Poisson algebras and Yang-Baxter equations

We connect generalizations of Poisson algebras with the classical and associative Yang-Baxter equations. In particular, we prove that solutions of the classical Yang-Baxter equation on a vector space V are equivalent to ``twisted'' Poisson algebra structures on the tensor algebra TV. Here, ``twisted'' refers to working in the category of graded vector spaces equipped with S_n-actions in degree n. We show that the associative Yang-Baxter equation is similarly related to the double Poisson algebras of Van den Bergh. We generalize to L-infinity-algebras and define ``infinity'' versions of Yang-Baxter equations and double Poisson algebras. The proofs are based on the observation that Lie is essentially unique among quadratic operads having a certain distributivity property over the commutative operad; we also give a L-infinity generalization. In the appendix, we prove a generalized version of Schur-Weyl duality, which is related to the use of nonstandard S_n-module structures on the n-th tensor power of V.
Protori and Torsion-Free Abelian Groups

The Resolution Theorem for Compact Abelian Groups is applied to show that the profinite subgroups of a finite-dimensional compact connected abelian group (protorus) which induce tori quotients comprise a lattice under intersection (meet) and $+$ (join), facilitating a proof of the existence of a universal resolution. A finite rank torsion-free abelian group $X$ is algebraically isomorphic to a canonical dense subgroup $X_G$ of its Pontryagin dual $G$. A morphism between protori lifts to a product morphism between the universal covers, so morphisms in the category can be studied as pairs of maps: homomorphisms between finitely generated profinite abelian groups and linear maps between finite-dimensional real vector spaces. A concept of non-Archimedean dimension is introduced which acts a useful invariant for classifying protori.
No de Sitter invariant vacuum in massive gravity theory with ghost

In this letter we point out that the massive gravity theory with a graviton ghost mode in de Sitter background cannot possess a de Sitter invariant vacuum state. In order to avoid a negative norm state, we must associate the creation operator of the ghost mode with a negative-energy mode function instead of a positive-energy one as the mode function. Namely, we have to adopt a different procedure of quantization for a ghost. When a theory has a symmetry mixing a ghost mode with ordinary non-ghost modes, the choice of a ghost mode is not unique. However, quantization of a ghost is impossible without specifying a choice of ghost mode, which breaks the symmetry. For this reason, the vacuum state cannot respect the symmetry. In the massive gravity theory with a graviton ghost mode in de Sitter background, the ghost is the helicity-0 mode of the graviton. This ghost mode is mixed with the other helicity graviton modes under the action of de Sitter symmetry. Therefore, there is no de Sitter invariant vacuum in such models. This leads to an interesting possibility that non-covariant cutoff of the low energy effective theory may naturally arise. As a result, the instability due to the pair production of a ghost and normal non-ghost particles gets much milder and that the model may escape from being rejected.
The Unevolved Main Sequence of Nearby Field Stars and the Open Cluster Distance Scale

The slope and zero point of the unevolved main sequence as a function of metallicity are investigated using a homogeneous catalog of nearby field stars with absolute magnitudes defined with revised Hipparcos parallaxes, Tycho-2 photometry, and precise metallicities from high-dispersion spectroscopy. (B - V) –temperature relations are derived from 1746 stars between [Fe/H] = -0.5 and +0.6 and 372 stars within 0.05 dex of solar abundance; for Teff = 5770 K, the solar color is B - V = 0.652 ± 0.002 (SEM). From over 500 cool dwarfs between [Fe/H] = -0.5 and +0.5, Δ ( B - V ) / Δ Fe / H at fixed MV = 0.213 ± 0.005, with a very weak dependenceupon the adopted main-sequence slope with B - V at a given [Fe/H]. At Hyades metallicity, this translates into Δ M V / Δ Fe / H at fixed B - V = 0.98 ± 0.02, midway between the range of values empirically derived from smaller and/or less homogenous samples and model isochrones. From field stars of similar metallicity, the Hyades ([Fe/H] = +0.13) with no reddening has (m - M)0 = 3.33 ± 0.02 and M67, with E(B - V) = 0.041, AV = 3.1E(B - V), and [Fe/H] = 0.00, has (m - M)0 = 9.71 ± 0.02 (SEM), where the errors quoted refer to internal errors alone. At the extreme end of the age and metallicity scale, with E(B - V) = 0.125 ± 0.025 and [Fe/H] = +0.39 ± 0.06, comparison of the fiducial relation for NGC 6791 to 19 field stars with (B - V) above 0.90 and [Fe/H] = +0.25 or higher, adjusted to the metallicity of NGC 6791, leads to (m - M)0 = 13.07 ± 0.09, internal and systematic errors included.
Asymptotic Analysis of the Mean Squared Displacement under Fractional Memory Kernels

The generalized Langevin equation (GLE) is a universal model for particle velocity in a viscoelastic medium. In this paper, we consider the GLE family with fractional memory kernels. We show that, in the critical regime where the memory kernel decays like $1/t$ for large $t$, the mean squared displacement (MSD) of particle motion grows linearly in time up to a slowly varying (logarithm) term. Moreover, we establish the well-posedness of the GLE in this regime. This solves an open question from [Mckinley 2018 Anomalous] and completes the answer to the conjecture put forward in [Morgado 2002 Relation] on the relationship between memory kernel decay and anomalously diffusive behavior. Under slightly stronger assumptions on the memory kernel, we construct an Abelian-Tauberian framework that leads to robust bounds on the deviation of the MSD around its asymptotic trend. This bridges the gap between the GLE memory kernel and the spectral density of anomalously diffusive particle motion characterized in [Didier 2017 Asymptotic].
Higher order mean curvatures of SAC half-lightlike submanifolds of indefinite almost contact manifolds

We introduce higher order mean curvatures of screen almost conformal (SAC) half-lightlike submanifolds of indefinite contact manifolds, admitting a semi-symmetric non-metric connection, and use them to generalize some known results of [6]. Also, we derive a new set of integration formulae via the divergence of some special vector fields tangent to this submanifold. Several examples are also included to illustrate the main concepts.
Chronological operator-valued Feynman-Kac formulae for generalized fractional evolutions

We study the generalized fractional linear problem $D^{\nu}_{a+*} f(x) =A(x)f(x)+g(x)$, where $D^{\nu}$ is an arbitrary mixture of Caputo derivatives of order at most one and $A(x)$ a family of operators in a Banach space generating strongly continuous semigroups. For time homogeneous case, when $A(x)$ does not depend on time $x$, the solution is expressed by the generalized operator-valued Mittag-Leffler function. For the more involved time-dependent case we use the method of non-commutative operator-valued Feynman-Kac formula in combination with the probabilistic interpretation of Caputo derivatives suggested recently by the author to find the general integral representation of the solutions, which are new even for the case of the standard Caputo derivative $D^{\beta}_{a+*}$. In the point of view adopted here we analyse the fractional equations not as some 'exotic evolutions', but rather as 'standard' stationary problems leading to the stationary non-commutative operator-valued Feynman-Kac representation.
From unicellular fatgraphs to trees

In this paper we study the minimum number of reversals needed to transform a unicellular fatgraph into a tree. We consider reversals acting on boundary components, having the natural interpretation as gluing, slicing or half-flipping of vertices. Our main result is an expression for the minimum number of reversals needed to transform a unicellular fatgraph to a plane tree. The expression involves the Euler genus of the fatgraph and an additional parameter, which counts the number of certain orientable blocks in the decomposition of the fatgraph. In the process we derive a constructive proof of how to decompose non-orientable, irreducible, unicellular fatgraphs into smaller fatgraphs of the same type or trivial fatgraphs, consisting of a single ribbon. We furthermore provide a detailed analysis how reversals affect the component-structure of the underlying fatgraphs. Our results generalize the Hannenhalli-Pevzner formula for the reversal distance of signed permutations.
Temporal stability of polymorphic Arctic charr parasite communities reflects sustained divergent trophic niches

Abstract Polymorphic Arctic charr Salvelinus alpinus populations frequently display distinct differences in habitat use, diet, and parasite communities. Changes to the relative species densities and composition of the wider fish community have the potential to alter the habitat niche of sympatric Arctic charr populations. This study evaluated the temporal stability of the parasite community, diet, and stable isotopes (δ13C, δ15N) of three sympatric Arctic charr morphs (piscivore, benthivore, and planktivore) from Loch Rannoch, Scotland, in relation to changes to the fish community. All Arctic charr morphs displayed distinct differences in parasite communities, diet, and stable isotope signatures over time, despite the establishment of four new trophically transmitted parasite taxa, and increased fish and zooplankton consumption by the piscivorous and planktivore morphs, respectively. Native parasite prevalence also increased in all Arctic charr morphs. Overall, Loch Rannoch polymorphic Arctic charr morph populations have maintained their distinct trophic niches and parasite communities through time despite changes in the fish community. This result indicates that re‐stocking a native fish species has the potential to induce shifts in the parasite community and diet of Arctic charr morphs.
Output Consensus of Networked Hammerstein and Wiener Systems

In this paper we consider the output consensus problem of networked Hammerstein and Wiener systems in a noisy environment. The Hammerstein or Wiener system is assumed to be open-loop stable, and its static nonlinearity is allowed to grow up but not faster than a polynomial. A control algorithm based on the distributed stochastic approximation algorithm with expanding truncations is designed and it is shown that under the designed control the output consensus is achieved. The numerical simulation given in the paper justifies the theoretical assertions.
Stability Results for Vertex Turán Problems in Kneser Graphs

The vertex set of the Kneser graph $K(n,k)$ is $V = \binom{[n]}{k}$ and two vertices are adjacent if the corresponding sets are disjoint. For any graph $F$, the largest size of a vertex set $U \subseteq V$ such that $K(n,k)[U]$ is $F$-free, was recently determined by Alishahi and Taherkhani, whenever $n$ is large enough compared to $k$ and $F$. In this paper, we determine the second largest size of a vertex set $W \subseteq V$ such that $K(n,k)[W]$ is $F$-free, in the case when $F$ is an even cycle or a complete multi-partite graph. In the latter case, we actually give a more general theorem depending on the chromatic number of $F$.
Intersections of two Grassmannians in $\mathbf{P}^9$

We study the intersection of two copies of $\mathrm{Gr}(2,5)$ embedded in $\mathbf{P}^9$, and the intersection of the two projectively dual Grassmannians in the dual projective space. These intersections are deformation equivalent, derived equivalent Calabi-Yau threefolds. We prove that generically they are not birational. As a consequence, we obtain a counterexample to the birational Torelli problem for Calabi-Yau threefolds. We also show that these threefolds give a new pair of varieties whose classes in the Grothendieck ring of varieties are not equal, but whose difference is annihilated by a power of the class of the affine line. Our proof of non-birationality involves a detailed study of the moduli stack of Calabi-Yau threefolds of the above type, which may be of independent interest.
Black hole evaporation in conformal gravity

We study the formation and the evaporation of a spherically symmetric black hole in conformal gravity. From the collapse of a spherically symmetric thin shell of radiation, we find a singularity-free non-rotating black hole. This black hole has the same Hawking temperature as a Schwarzschild black hole with the same mass, and it completely evaporates either in a finite or in an infinite time, depending on the ensemble. We consider the analysis both in the canonical and in the micro-canonical statistical ensembles. Last, we discuss the corresponding Penrose diagram of this physical process.
Graphical representation of the partition function of a one-dimensional δ-function Bose gas

The one-dimensional repulsive δ-function bose system is studied. By only using the Bethe ansatz equation, n-particle partition functions are exactly calculated. From this expression for the n-particle partition function, the n-particle cluster integral is derived. The results completely agree with those of the thermal Bethe ansatz (TBA). This directly proves the validity of the TBA. The theory of partitions and graphs is used to simplify the discussion.
Homogenization in BV of a model for layered composites in finite crystal plasticity

Abstract In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider materials arranged into periodically alternating thin horizontal strips of an elastically rigid component and a softer one with one active slip system. The energies arising from these modeling assumptions are of integral form, featuring linear growth and non-convex differential constraints. We approach this non-standard homogenization problem via Gamma-convergence. A crucial first step in the asymptotic analysis is the characterization of rigidity properties of limits of admissible deformations in the space BV of functions of bounded variation. In particular, we prove that, under suitable assumptions, the two-dimensional body may split horizontally into finitely many pieces, each of which undergoes shear deformation and global rotation. This allows us to identify a potential candidate for the homogenized limit energy, which we show to be a lower bound on the Gamma-limit. In the framework of non-simple materials, we present a complete Gamma-convergence result, including an explicit homogenization formula, for a regularized model with an anisotropic penalization in the layer direction.
Relaxation of ferroelectric states in 2D distributions of quantum dots: EELS simulation

The relaxation time of collective electronic states in a 2D distribution of quantum dots is investigated theoretically by simulating EELS experiments. From the numerical calculation of the probability of energy loss of an electron beam, traveling parallel to the distribution, it is possible to estimate the damping time of ferroelectric-like states. We generate this collective response of the distribution by introducing a mean field interaction among the quantum dots, and then, the model is extended incorporating effects of long-range correlations through a Bragg–Williams approximation. The behavior of the dielectric function, the energy loss function, and the relaxation time of ferroelectric-like states is then investigated as a function of the temperature of the distribution and the damping constant of the electronic states in the single quantum dots. The robustness of the trends and tendencies of our results indicate that this scheme of analysis can guide experimentalists to develop tailored quantum dots distributions for specific applications.
Multiplicities of cohomological automorphic forms on $\mathrm{GL}_2$ and mod $p$ representations of $\mathrm{GL}_2(\mathbb{Q}_p)$

We prove a new upper bound for the dimension of the space of cohomological automorphic forms of fixed level and growing parallel weight on $\mathrm{GL}_2$ over a number field which is not totally real, improving the one obtained by Marshall. The main tool of the proof is the mod $p$ representation theory of $\mathrm{GL}_2(\mathbb{Q}_p)$ as started by Barthel-Livne and Breuil, and developed by Paskunas.
IDIOPATHIC TASTE IMPAIRMENT IN A YOUNG WOMAN: A CASE REPORT

ABSTRACT Background: The underlying cause of taste impairment includes damage in the central or peripheral nervous system, nutrition deficiency, systemic disease, or idiopathic. This condition usually occurs with advancing age. Taste alteration may affect the patient’s psychological aspect and causing malnutrition or even develop into more serious health problems. Purpose: This report aims to evaluate an unusual partial ageusia in a young woman and to review articles with idiopathic taste disorders. Case: A 33-year-old woman was referred to the Department of Oral Medicine from the neurology department with a primary diagnosis of migraine and median nerve mononeuropathy. The patient also complained of loss of tastes (salty, bitter, and sour) accompanied by numbness on the palate and left buccal mucosa for the past two weeks. Case Management: The patient was given a 0.12% chlorhexidine digluconate mouthwash and 25 mg zinc tablets twice a day. After 2 weeks, she can identify bitter, and followed by sweet and sour in the next few weeks, as well as improvement of the numbness. Eighteen studies of idiopathic taste disorders from 1991-2021 have been reported in the literature. Conclusion: Taste disorders with unknown aetiology may happen in young individuals. Zinc has been proven as a beneficial micronutrient to treat patients with idiopathic taste impairment. Dentists should consider this approach to resolve the symptoms and accelerate the healing process of possible co-occurrence systemic diseases. Keywords: Ageusia, idiopathic, Taste dysfunction, Treatment
Strongly magnetized cold degenerate electron gas: Mass-radius relation of the magnetized white dwarf

We consider a relativistic, degenerate electron gas at zero temperature under the influence of a strong, uniform, static magnetic field, neglecting any form of interactions. Since the density of states for the electrons changes due to the presence of the magnetic field (which gives rise to Landau quantization), the corresponding equation of state also gets modified. In order to investigate the effect of very strong magnetic field, we focus only on systems in which a maximum of either one, two, or three Landau level(s) is/are occupied. This is important since, if a very large number of Landau levels are filled, it implies a very low magnetic field strength which yields back Chandrasekhar's celebrated nonmagnetic results. The maximum number of occupied Landau levels is fixed by the correct choice of two parameters, namely, the magnetic field strength and the maximum Fermi energy of the system. We study the equations of state of these one-level, two-level, and three-level systems and compare them by taking three different maximum Fermi energies. We also find the effect of the strong magnetic field on the mass-radius relation of the underlying star composed of the gas stated above. We obtain an exciting result that it is possible to have an electron-degenerate static star, namely, magnetized white dwarfs, with a mass significantly greater than the Chandrasekhar limit in the range 2.3-2.6M(circle dot), provided it has an appropriate magnetic field strength and central density. In fact, recent observations of peculiar type Ia supernovae-SN 2006gz, SN 2007if, SN 2009dc, SN 2003fg-seem to suggest super-Chandrasekhar-mass white dwarfs with masses up to 2.4-2.8M(circle dot) as their most likely progenitors. Interestingly, our results seem to lie within these observational limits.
A YOUNG ECLIPSING BINARY AND ITS LUMINOUS NEIGHBORS IN THE EMBEDDED STAR CLUSTER Sh 2-252E

We present a photometric and light curve analysis of an eccentric eclipsing binary in the K2 Campaign 0 field, which resides in Sh 2-252E, a young star cluster embedded in an H ii region. We describe a spectroscopic investigation of the three brightest stars in the crowded aperture to identify which is the binary system. We find that none of these stars are components of the eclipsing binary system, which must be one of the fainter nearby stars. These bright cluster members all have remarkable spectra: Sh 2-252a (EPIC 202062176) is a B0.5 V star with razor sharp absorption lines, Sh 2-252b is a Herbig A0 star with disk-like emission lines, and Sh 2-252c is a pre-main-sequence star with very red color.
Temporary Behavioral Responses to Playbacks by a Pest Parrot and Implications for Management

Human-wildlife interactions continue to increase due to anthropogenic disturbances, with some interactions resulting in conflict. Leveraging a taxa’s bias for a particular sensory cue is a promising management avenue for reducing the potential and realized negative consequences of human-wildlife conflict. For instance, many avian species heavily depend on acoustic communication, and acoustic cues can provide opportunities to reduce conflict with various avian species. The monk parakeet (Myiopsitta monachus) is a gregarious parrot native to South America that has established populations worldwide and is considered an urban and agricultural pest in parts of its native and introduced ranges. We conducted playback experiments with a captive population of monk parakeets to evaluate auditory cues that may be useful for designing management protocols. Our experiment evaluated the efficacy of two stimuli: predator vocalizations as potential repulsion and conspecific vocalizations as potential attraction stimuli for parakeets. We measured two responses: (1) categorical group-level behavioral responses and (2) time to cease vigilance and return to behavior prior to playback. In the repulsion playbacks, monk parakeets were repelled by predator vocalizations in 80% of trials and took longer to cease vigilance and return to baseline behavior compared to attraction playbacks. In the attraction playbacks, monk parakeets exhibited vigilant behavior and weak or no attraction to the stimulus, with attraction only being observed in 10% of trials. Our results demonstrate that predator playbacks may be particularly useful for completing management objectives, such as temporary removal from a location.
Combinatorial $\alpha$-curvatures and $\alpha$-flows on polyhedral surfaces, I

We introduce combinatorial $\alpha$-curvature for piecewise linear metrics on polyhedral surfaces, which is a generalization of the classical combinatorial curvature on polyhedral surfaces. Then we prove the global rigidity of $\alpha$-curvature with respect to the discrete conformal factors. To study the corresponding Yamabe problem of $\alpha$-curvature, we introduce the combinatorial $\alpha$-Yamabe flow and combinatorial $\alpha$-Calabi flow for piecewise linear metrics on surfaces. To handle the possible singularities along the flows, we do surgery on the flows by flipping. Then we prove that if $\alpha\chi(S)\leq 0$, there exists a piecewise linear metric with constant combinatorial $\alpha$-curvature on a polyhedral surface $S$, which is a parameterized generalization of Gu-Luo-Sun-Wu's discrete uniformization theorem. We further prove that the combinatorial $\alpha$-Yamabe flow and $\alpha$-Calabi flow with surgery exists for all time and converges to a piecewise linear metric with constant combinatorial $\alpha$-curvature for any initial piecewise linear metric if $\alpha\chi(S)\leq 0$.