Miracle-dz/UniFAR-FTUs huggingface dataset:
Newforms and Spectral Multiplicities for $\Gamma_0(9)$

The goal of this paper is to explain certain experimentally observed properties of the (cuspidal) spectrum and its associated automorp hic forms (Maass waveforms) on the congruence subgroup Γ0(9). The first property is that the spectrum possesses multiplicities in the so-called new part, where it was previous ly believed to be simple. The second property is that the spectrum does not contain any “ge nuin ly new” eigenvalues, in the sense that all eigenvalues of Γ0(9) appear in the spectrum of some congruence subgroup of lower level. The main theorem in this paper gives a precise decomposition of the spectrum of Γ0(9) and in particular we show that the genuinely new part is empty . We also prove that there exist an infinite number of eigenvalues of Γ0(9) where the corresponding eigenspace is of dimension at least two and has a basis of pairs of Hecke-Maa ss newforms which are related to each other by a character twist. These forms are no n-holomorphic analogues of modular forms with inner twists and also provide explicit (affirmative) examples of a conjecture stating that if the Hecke eigenvalues of two “gen eric” Maass newforms coincide on a set of primes of density 2 then they have to be related by a character twist.
Isochronous Cosmologies

The possibility has been recently demonstrated to manufacture (nonrelativistic, Hamil- tonian) many-body problems which feature an isochronous time evolution with an arbitrarily assigned period T yet mimic with good approximation, or even exactly, any given many-body problem (within a large, physically relevant, class) over times ˜ T which may also be arbitrarily large (but of course such that ˜ T < T ). Purpose and scope of this paper is to explore the possibility to extend this ﬁnding to a general relativity context. For simplicity we restrict our consideration to the case of homogeneous and isotropic metrics and show that, via an approach analogous to that used for the nonrelativistic many-body problem, a class of homogeneous and isotropic cyclic solutions of Einstein’s equations may be obtained. For these solutions the duration of the cycles does not de- pend on the initial conditions, so we call these models isochronous cosmologies . We give a physical interpretation of such metrics and in particular we show that they may behave arbitrarily closely, or even identically , to the Friedman-Robertson-Walker solutions of Einstein’s equations for an arbitrarily long time (of course shorter than their period, which can also be assigned arbitrarily ), so that they may reproduce all the satisfac-tory phenomenological features of the standard cosmological Λ-CDM model in a portion of their cycle; while these isochronous cosmologies may be geodesically complete and therefore singularity-free .
Bubbling analysis and geometric convergence results for free boundary minimal surfaces

We investigate the limit behaviour of sequences of free boundary minimal hypersurfaces with bounded index and volume, by presenting a detailed blow-up analysis near the points where curvature concentration occurs. Thereby, we derive a general quantization identity for the total curvature functional, valid in ambient dimension less than eight and applicable to possibly improper limit hypersurfaces. In dimension three, this identity can be combined with the Gauss-Bonnet theorem to provide a constraint relating the topology of the free boundary minimal surfaces in a converging sequence, of their limit, and of the bubbles or half-bubbles that occur as blow-up models. We present various geometric applications of these tools, including a description of the behaviour of index one free boundary minimal surfaces inside a 3-manifold of non-negative scalar curvature and strictly mean convex boundary. In particular, in the case of compact, simply connected, strictly mean convex domains in $\mathbb{R}^3$ unconditional convergence occurs for all topological types except the disk and the annulus, and in those cases the possible degenerations are classified.
Compressed Sensing for Analog Signals

In this paper we develop a general theory of compressed sensing for analog signals, in close similarity to prior results for vectors in finite dimensional spaces that are sparse in a given orthonormal basis. The signals are modeled by functions in a reproducing kernel Hilbert space. Sparsity is defined as the minimal number of terms in expansions based on the kernel functions. Minimizing this number is under certain conditions equivalent to minimizing an atomic norm, the pre-dual of the supremum norm for functions in the Hilbert space. The norm minimizer is shown to exist based on a compactness argument. Recovery based on minimizing the atomic norm is robust and stable, so it provides controllable accuracy for recovery when the signal is only approximately sparse and the measurement is corrupted by noise. As applications of the theory, we include results on the recovery of sparse bandlimited functions and functions that have a sparse inverse short-time Fourier transform.
Efficiency of martingale methods in recapture studies

SUMMARY The asymptotic variances of various estimators of the population size from a recapture study are calculated. The estimation methods compared are maximum likelihood and a class of natural martingale estimators with both time variation and behavioural response. It is found that (i) the martingale methods appropriate for time variation or behavioural response are fully efficient, (ii) there is no loss of efficiency at all in allowing for time variation, (iii) there is large loss of efficiency in allowing for behavioural response, (iv) there is a natural martingale method that allows for both time variation and behavioural response.
Optimal strong approximation for quadratic forms

For a non-degenerate integral quadratic form $F(x_1, \dots , x_d)$ in $d\geq5$ variables, we prove an optimal strong approximation theorem. Let $\Omega$ be a fixed compact subset of the affine quadric $F(x_1,\dots,x_d)=1$ over the real numbers. Take a small ball $B$ of radius $0 0$. Finally assume that an integral vector $(\lambda_1, \dots, \lambda_d) $ mod $m$ is given. Then we show that there exists an integral solution $X=(x_1,\dots,x_d)$ of $F(X)=N$ such that $x_i\equiv \lambda_i \text{ mod } m$ and $\frac{X}{\sqrt{N}}\in B$, provided that all the local conditions are satisfied. We also show that 4 is the best possible exponent. Moreover, for a non-degenerate integral quadratic form in 4 variables we prove the same result if $N$ is odd and $N\gg_{\delta,\Omega} (r^{-1}m)^{6+\epsilon}$. Based on our numerical experiments on the diameter of LPS Ramanujan graphs and the expected square root cancellation in a particular sum that appears in Remark~\ref{evidence}, we conjecture that the theorem holds for any quadratic form in 4 variables with the optimal exponent $4$.
Matched-filtering and parameter estimation of ringdown waveforms

Using recent results from numerical relativity simulations of nonspinning binary black hole mergers, we revisit the problem of detecting ringdown waveforms and of estimating the source parameters, considering both LISA and Earth-based interferometers. We find that Advanced LIGO and EGO could detect intermediate-mass black holes of mass up to {approx}10{sup 3}M{sub {center_dot}} out to a luminosity distance of a few Gpc. For typical multipolar energy distributions, we show that the single-mode ringdown templates presently used for ringdown searches in the LIGO data stream can produce a significant event loss (>10% for all detectors in a large interval of black hole masses) and very large parameter estimation errors on the black hole's mass and spin. We estimate that more than {approx}10{sup 6} templates would be needed for a single-stage multimode search. Therefore, we recommend a ''two-stage'' search to save on computational costs: single-mode templates can be used for detection, but multimode templates or Prony methods should be used to estimate parameters once a detection has been made. We update estimates of the critical signal-to-noise ratio required to test the hypothesis that two or more modes are present in the signal and to resolve their frequencies, showing that second-generation Earth-based detectors andmore » LISA have the potential to perform no-hair tests. « less
Localization for quasiperiodic Schrödinger operators with multivariable Gevrey potential functions

We consider an integer lattice quasiperiodic Schrodinger operator. The underlying dynamics is either the skew-shift or the multi-frequency shift by a Diophantine frequency. We assume that the potential function belongs to a Gevrey class on the multi-dimensional torus. Moreover, we assume that the potential function satisfies a generic transversality condition, which we show to imply a Lojasiewicz type inequality for smooth functions of several variables. Under these assumptions and for large coupling constant, we prove that the associated Lyapunov exponent is positive for all energies, and continuous as a function of energy, with a certain modulus of continuity. Moreover, in the large coupling constant regime and for an asymptotically large frequency - phase set, we prove that the operator satisfies Anderson localization.
An Assessment of Currency Exposure of Non-Financial Firms in ASEAN-4: Insights using the Stock Returns and Cash Flow Methodologies

This study examines the extent and nature of foreign exchange exposure in 405 listed corporations operating in the ASEAN-4 nations, Indonesia, Malaysia, Singapore, and Thailand. The study period of 23 years, from 1995 to 2017, covers the two major crisis periods, the Asian financial crisis (AFC) of 1997 and the global financial crisis (GFC) of 2008. Our study improves on earlier work by using two alternative assessment methods, i.e., stock returns (SR) and cash flow (CF) methods. We report several interesting and noteworthy results. First, we find that the stock returns approach results in a higher incidence of exchange rate exposure relative to the cash flow method. Specifically, about 65% and 28% of the total ASEAN-4 firms had significant exposure to all currencies under the stock returns and cash flow methods, respectively. Second, we find the sample firms to have predominant exposure to the US dollar, signifying the important role played by the United States (US) as the major trading partner of the ASEAN-4. Third, when evaluating time-varying exposure, we find that the incidence of the exchange rate exposure is event-specific. Most of our sample firms were highly exposed to exchange rates during the mid-points of the AFC and the GFC.
Editorial H‐score as a metric of inner authenticity for national scientific journals—Pilot study for the field of pedagogy

There is evidence that national scientific journals are important for local communities despite their limited audience due to national languages and topics, like in pedagogy. However, it is not easy to assess the level of scientific rigour of local journals, as most do not have available scientometric data and are often published in minority languages. We hypothesize that a possible manifestation of a latent trait of inner authenticity of the scientific journal (meaning the journal is accepted by a community interested in developing the field which conducts internationally accepted research) could be H‐index of the editorial board members. To test this approach, we evaluated H‐index and gender of editorial board members (n = 490) from 17 Czech and Slovak national science‐oriented scientific pedagogical journals which were not indexed or indexed in Erih+ or Scopus, and compared this with the five lowest‐rated journals from the same field indexed in the Web of Science (WoS) database. The H‐index of editorial board members was somewhat higher in indexed journals with those from WoS showing higher scores, and the number of board members with no discernable H‐index was far greater in non‐indexed journals. Editorial boards of journals indexed in WoS were mostly male, compared to a dominance of women on boards of non‐indexed journals. Acknowledging the limited sample, it appears that the H‐index of editorial board members may be a way to value national scientific journals.
Gas density gradient for three dark interstellar clouds

A grid of models has been constructed of the surface brightness of selected transitions of interstellar formal-dehyde for three interstellar clouds. The grid included radial gas density gradients over a considerable range from uniform to very steep. The model results were then compared to observations of the interstellar dark clouds B361, L183, and L134. In all three cases, the comparison indicates that the gas is centrally condensed and follows a gradient in density which closely approximates an inverse square law. This result offers a hint that the dust may be more centrally condensed than the gas in B361.
Comparison of Antenatal Maternal Mental Representations Between Depressed and Non-depressed of Pregnant Mothers

Background: Depression is the most prevalent mental health problem in the pregnant women with significant implications for mother and infant’s health. The content of maternal antenatal representations may be related to their depressive symptoms during the perinatal period. Objectives: This study aimed to compare maternal mental representations between depressed and non-depressed groups of pregnant women. Methods: In a causal-comparative study, participants were selected using an inverse stratified sampling method among pregnant women in the last trimester of pregnancy (depressed mothers = 93, and non-depressed mothers = 97). All participants completed Edinburgh Postnatal Depression Scale (EPDS), Dépistage Anténatal de la Dépression Postnatale (DADP), and semi-structure Interview-R after the consent form. Independent- samples t-test, Two-way ANOVA, and Pearson correlation coefficient were applied to compare maternal mental representations subscales between groups, using SPSS-26. Results: The results showed significantly fewer positive ratings for all subscales of Interview-R, including child, partner, self as mother, and mother as own mother in the depressed group (P < 0.05). In the group of depressed mothers, 57% and 32% of the correlations among the representations of child/self as mother and child/partner were significant, while in the non-depressed group, 28% and 48% of the correlations between child/self as mother and child/ partner were significant (P < 0,05), respectively. The characteristics of self as mother and own mother showed significant differences in the depressed group compared to the non-depressed group (P < 0.05). Conclusions: Depressed pregnant mothers are less likely to differentiate themselves from their children compared to non-depressed pregnant mothers. Besids, depressed pregnant mothers perceive themselves as mothers more positively than their own mothers, while the opposite is true for non-depressed pregnant mothers.
Diet quality impairs male and female reproductive performance and affects the opportunity for selection in an insect model

Abstract Environmental factors can have profound effects on the strength and direction of selection and recent studies suggest that such environment‐dependent selection can be sex‐specific. Sexual selection theory predicts that male fitness is more condition dependent compared to female fitness, suggesting that male fitness is more sensitive to environmental stress. However, our knowledge about the effect of environmental factors on sex‐specific reproductive performance and on sex differences in the opportunity for selection is still very limited. In the present study, we investigated the sex‐specific effects of diet quality (yeast deprivation and flour type) in the red flour beetle Tribolium castaneum . Specifically, we manipulated yeast supplementation in wheat and whole‐wheat flour in competition assays allowing us to test for sex‐specific effects of food quality (i) on reproductive success and (ii) on the opportunity for selection. Our data show that yeast deprivation in wheat flour had significantly negative effects on body mass and reproductive success of both sexes, while high‐quality flour (whole‐wheat flour) was able to buffer the negative impact to a large extent. Importantly, our data suggest no sex‐specific effect of dietary stress on reproductive success because the magnitude of the negative effect of yeast deprivation was similar for males and females. Moreover, our study demonstrates that low food quality inflated the opportunity for selection and did not differ between sexes neither under benign nor stressful dietary conditions. We discuss the implications of our findings for the adaptation to stressful environments.
Impact of supplementation of semen extender with antioxidants on quality of cooled or cryopreserved Marwari stallion spermatozoa

The aim of the present study was to evaluate the effects of supplementation of semen extender with two antioxidants namely Ascorbic acid (AA @ 0.9 g/L), Glutathione (GSH @ 2.5 mM), and combination of both (AA @ 0.9 g/L + GSH @ 2.5 mM) either in alone or in combination on the quality of cooled or cryopreserved Marwari stallion spermatozoa. For this purpose, a total of 24 ejaculates were collected from four adult and fertile Marwari stallions (6 ejaculates from each stallion) using an artificial vagina. Each freshly ejaculated semen sample was investigated for the semen quality parameters, viz. colour, consistency, total volume, gel volume, gel free volume, pH, progressive sperm motility, sperm concentration, sperm viability, sperm plasma membrane integrity, acrosomal integrity and DNA integrity. In the freshly ejaculated semen, no significant variation was found among individual stallions for various semen quality parameters except in sperm concentration. Pre-freeze and post-thaw semen evaluation revealed that the values for the most of the semen quality parameters were significantly higher in the semen extender being treated with the combination (AA @ 0.9 g/L +GSH @ 2.5 mM) of antioxidants group rather than AA and GSH alone or control. Addition of AA (0.9 g/L) and GSH (2.5 mM) to the freezing extender improved equine pre-freeze and post-thaw semen quality with the superiority of control group which indicates the beneficial role of supplementation of antioxidants to the stallion semen during cryopreservation process.
Non-Exact Symplectic Cobordisms Between Contact 3-Manifolds

We show that the pre-order defined on the category of contact manifolds by arbitrary symplectic cobordisms is considerably less rigid than its counterparts for exact or Stein cobordisms: in particular, we exhibit large new classes of contact 3-manifolds which are symplectically cobordant to something overtwisted, or to the tight 3-sphere, or which admit symplectic caps containing symplectically embedded spheres with vanishing self-intersection. These constructions imply new and simplified proofs of several recent results involving fillability, planarity and non-separating contact type embeddings. The cobordisms are built from generalized symplectic handles which have cores that are arbitrary symplectic surfaces with boundary and co-cores that are symplectic disks or annuli; these can be attached to contact 3-manifolds along sufficiently large neighborhoods of transverse links or pre-Lagrangian tori. We also sketch a construction of J-holomorphic foliations in these cobordisms and formulate a conjecture regarding maps induced on Embedded Contact Homology with twisted coefficients.
Generalized quantum Zeno dynamics and ergodic means

We prove the existence of uniform limits for certain sequences of products of contractions and elements of a family of uniformly continuous propagators acting on a Hilbert or a Banach space. From the point of view of Quantum Physics, the considered sequences can represent the evolution of a system whose dynamics, described by a continuous propagator, is disturbed by a sequence of generic quantum operations (e.g., projective measurements or unitary pulses). This includes and also generalizes the so-called quantum Zeno dynamics. The time-evolution obtained from the limits of the considered sequences are described by propagators generated by ergodic means. The notion of such ergodic means is generalized in this paper to also include propagators of time-dependent generators, and thus our results can be used to develop new forms of active decoherence suppression. In a similar way, we also consider the effective time-evolution obtained from adding to the possibly time-dependent generator of the original propagator a generator of a uniformly continuous contraction semi-group with asymptotically increasing weight in the sum. By proving a generalized adiabatic theorem, it is shown that also for this set-up the resulting time-evolution is governed by a suitable ergodic mean.
Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying Random Walks and Compound Poisson Processes

We propose a class of strongly efficient rare event simulation estimators for random walks and compound Poisson processes with a regularly varying increment/jump-size distribution in a general large deviations regime. Our estimator is based on an importance sampling strategy that hinges on the heavy-tailed sample path large deviations result recently established in Rhee, Blanchet, and Zwart (2016). The new estimators are straightforward to implement and can be used to systematically evaluate the probability of a wide range of rare events with bounded relative error. They are "universal" in the sense that a single importance sampling scheme applies to a very general class of rare events that arise in heavy-tailed systems. In particular, our estimators can deal with rare events that are caused by multiple big jumps (therefore, beyond the usual principle of a single big jump) as well as multidimensional processes such as the buffer content process of a queueing network. We illustrate the versatility of our approach with several applications that arise in the context of mathematical finance, actuarial science, and queueing theory.
L^{\infty} a priori bounds for gradients of solutions to quasilinear inhomogenous fast-growing parabolic systems

We prove boundedness of gradients of solutions to quasilinear parabolic system, the main part of which is a generalization to p-Laplacian and its right hand side's growth depending on gradient is not slower (and generally strictly faster) than p - 1. This result may be seen as a generalization to the classical notion of a controllable growth of right hand side, introduced by Campanato, over gradients of p-Laplacian-like systems. Energy estimates and nonlinear iteration procedure of a Moser type are cornerstones of the used method.
Rational homotopy type of the space of immersions of a manifold in an euclidian space

Let $M$ be a simply-connected $m$ dimensional manifold of finite type and $k$ a positif integer. In this paper we show that the rational Betti numbers of each component of the space of immersions of $M$ in $\mathbb{R}^{m+k}$, have polynomial growth. As consequence, we deduce that, if $M$ is a manifold with Euler characteristic $\chi\left(M\right)\leq -2$, the Betti numbers of smooth embeddings, $Emb\left(M ,\mathbb{R}^{m+k}\right)$, have exponential growth if $k\geq m+1$. The main tool of this work is the construction of an explicit model of the space of immersions.