Miracle-dz/UniFAR-FTUs huggingface dataset:
Upper large deviations for maximal flows through a tilted cylinder

We consider the standard first passage percolation model in ℤd for d ≥ 2 and we study the maximal flow from the upper half part to the lower half part (respectively from the top to the bottom) of a cylinder whose basis is a hyperrectangle of sidelength proportional to n and whose height is h (n ) for a certain height function h . We denote this maximal flow by τ n (respectively φ n ). We emphasize the fact that the cylinder may be tilted. We look at the probability that these flows, rescaled by the surface of the basis of the cylinder, are greater than ν (v ) + e for some positive e , where ν (v ) is the almost sure limit of the rescaled variable τ n when n goes to infinity. On one hand, we prove that the speed of decay of this probability in the case of the variable τ n depends on the tail of the distribution of the capacities of the edges: it can decay exponentially fast with n d −1 , or with n d −1 min(n,h (n )), or at an intermediate regime. On the other hand, we prove that this probability in the case of the variable φ n decays exponentially fast with the volume of the cylinder as soon as the law of the capacity of the edges admits one exponential moment; the importance of this result is however limited by the fact that ν (v ) is not in general the almost sure limit of the rescaled maximal flow φ n , but it is the case at least when the height h (n ) of the cylinder is negligible compared to n .
Hilbert modules associated to parabolically induced representations of semisimple Lie groups

Given a measured space X with commuting actions of two groups G and H satisfying certain conditions, we construct a Hilbert C*(H)-module E(X) equipped with a left action of C*(G), which generalises Rieffel's construction of inducing modules. Considering G to be a semisimple Lie group and H to be the Levi component L of a parabolic subgroup P=LN, the Hilbert module associated to X=G/N encodes the P-series representations of G coming from parabolic subgroups associated to P. We provide several descriptions of this Hilbert module, corresponding to the classical pictures of P-series. We then characterise the bounded operators on E(G/N) that commute to the left action of C*(G) as central multipliers of C*(L) and interpret this result as a globalised generic irreducibility theorem. Finally, we establish the convergence of intertwining integrals on a dense subset of E(G/N).
Quantum groups, q-Boson algebras and quantized Weyl algebras

We give a unified construction of quantum groups, q-Boson algebras and quantized Weyl algebras and an action of quantum groups on quantized Weyl algebras. This enables us to give a conceptual proof of the semi-simplicity of the category $\mathcal{O}(B_q)$ introduced by T.Nakashima and the classification of all simple objects in it.
The hydrocarbon compounds sources in surface sediments of the Laptev Sea shelf

Rapid warming of the Arctic provokes large-scale degradation of permafrost on land terrestrial and in submarines. A vast amount of remobilized organic matter (OM) is involved in the modern biogeochemical cycle. Understanding of the fate of terrestrial OM moving from the land to the Arctic shelf is essential for predicting the potential feedback of Arctic ecosystems. In our research, an attempt was made to characterize the modern OM stored in the surface sediments of the Laptev Sea to estimate its composition variability and to identify the OM sources along with the “coastline outer shelf” profile. Here we discuss the OM features revealed by Rock-Eval pyrolysis (RE) and the distribution of nalkanes in combination with sediment grain-size analysis. The GC/MS records are directly comparable with RE data tracing the terrestrial OM along with the entire studied profile. However, we observe both a significant decline of terrestrial input and the rise of hydrobiont in the outer shelf zone. We assume that different OM sources may produce different ranges of RE values.
IJOMS Vol 19-4-37.indd

Introduction Orthodontically induced inflammatory root resorption (OIIRR)is an inevitable complication that difficult to predict before orthodontic treatment. There are two types of causes of OIIRR. One is a treatment specific factors, including prolonged treatment (1)and heavy correctional force(2). The other one is patient specific factors, including genetic elements (3), age(4), root abnormalities (2), a history of tooth trauma(5), and allergies (6). However, the mechanism underlying OIIRR remains unclear. In previous studies, it is demonstrated that nuclear factor kappa -B ligand(RANKL)and interleukin -6(IL -6) were detected in resorbed root and periodontal ligament (PDL)tissue subjecteded to heavy orthodontic force (7, 8). Furthermore, several studies reported that RANKL and IL -6 are induced from human PDL(hPDL)cells under the compressive force(CF)in vitro(9–11). Therefore, these cytokines are associated with OIIRR during orthodontic tooth movement. Transforming growth factor-β(TGF-β)signaling controls development and homeostasis of various somatic tissues. TGF-β is responsible for cell differentiation, proliferation, adhesion, apoptosis, and extracellular substrate production in fibroblasts and alveolar bone at the periCorrespondence to: Michiko Tsukada E-mail : mami17010@g. nihon-u.ac. jp doi:10.5466/ijoms.19. 278 Article History Abstract
Fractional order Taylor's series and the neo‐classical inequality

We prove the neo‐classical inequality with the optimal constant, which was conjectured by T. J. Lyons (‘Differential equations driven by rough signals’, Rev. Mat. Iberoamericana 14 (1998) 215–310). For the proof, we introduce the fractional order Taylor's series with residual terms. Their application to a particular function provides an identity that deduces the optimal neo‐classical inequality.
Brownian motion and anomalous diffusion revisited via a fractional Langevin equation

In this paper we revisit the Brownian motion on the basis of the fractional Langevin equation which turns out to be a particular case of the generalized Langevin equation introduced by Kubo in 1966. The importance of our approach is to model the Brownian motion more realistically than the usual one based on the classical Langevin equation, in that it takes into account also the retarding effects due to hydrodynamic back-flow, i.e. the added mass and the Basset memory drag. We provide the analytical expressions of the correlation functions (both for the random force and the particle velocity) and of the mean squared particle displacement. The random force has been shown to be represented by a superposition of the usual white noise with a ”fractional” noise. The velocity correlation function is no longer expressed by a simple exponential but exhibits a slower decay, proportional to t for long times, which indeed is more realistic. Finally, the mean squared displacement is shown to maintain, for sufficiently long times, the linear behaviour which is typical of normal diffusion, with the same diffusion coefficient of the classical case. However, the Basset history force induces a retarding effect in the establishing of the linear behaviour, which in some cases could appear as a manifestation of anomalous diffusion to be correctly interpreted in experimental measurements. Paper published in Modern Problems of Statistical Physics, Vol 8, pp. 3-23 (2009): a journal founded to the memory of Prof. Ascold N. Malakhov, see http://www.mptalam. org/i.html Brownian motion and anomalous diffusion revisited via a fractional Langevin equation 2
Evaluation of The Final Time and Velocity of a 100 m Run Under the Realistic Conditions

Abstract The aim of the research was to provide an analytical expression for the final time and velocity at the 100 m run, taking into account realistic conditions of the run, more precisely the effect of the wind and resistance of the medium (air). Combining the polynomial model for the distance vs time with the solution of the algebraic cubic equation, such an analytical expression was derived. The expression allowed to evaluate the dependence of the final time of the race on the wind velocity. This enabled the quantification of the time effect of the mentioned influences on the final time and velocity. It is possible to calculate the dependence of the sprinter’s velocity on expired running time for various wind velocities (from 0 up to ± 10 m/s) as well as determine the maximal running velocity vmax and corresponding time moment tmax. The results obtained were verified using split time data for six top sprinters: C. Lewis, M. Green, U. Bolt and F. Griffith-Joyner, E. Ashford and H. Drechsler. The results confirmed that it was possible to quantify the time effect of the influence of the wind velocity and resistance of the medium on the final time of the 100 m run. Although the applicability of the approach was tested using the data concerning top sprinters, the mathematical expressions involved are simple enough to be used by any coach to estimate the results of a sprinter under various weather conditions.
Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Absolute desingularization in characteristic zero

We present a survey on the recent progress with desingularization of quasi-excellent schemes of characteristic zero. Due to expository goals of the paper we concentrate on giving examples and outlining main ideas, and we refer to other sources for detailed proofs and technical details. This survey will be published in the proceedings of the conference "Motivic integration and its interactions with model theory and non-archimedean geometry" (ICMS, May 2008).
E‹cacy of MR Mammography (MRM) in Providing Preoperative Locoregional Information on Breast Cancer: Correlation between MRM and Histological Findings

Rationale and Objectives: To assess the e‹cacy of MRM in providing preoperative locoregional information on patients with breast cancer. Methods: MRI was performed on 62 female breast cancer patients. A 1.5T MR-system was used to acquire fat-suppressed T 1 WI, T 2 WI and dynamic-contrast-enhanced images with an SPGR pulse sequence. The extent of the cancer measured with MRM was con-ˆrmed histologically in all patients. Results: The size obtained from MRM correlated well with the size obtained histologically, including intraductal spread of cancer (R: 0.853). As for shape, the round W oval type evi-dent from MRM correlated more accurately (R: 0.934) than the ill-deˆned type associated with a linear and W or clumped enhanced area (R: 0.744). The diŠerence between the size obtained from MRM and the size obtained histologically, including IDS, was less than 15 mm in the majority of patients (93.5 z ). Conclusions: MRM accurately reveals the extent of cancer, including IDS, and is eŠec-tive at providing preoperative locoregional information for breast-conserving therapy for breast cancer.
Embedded Cobordism Categories and Spaces of Submanifolds

Galatius, Madsen, Tillmann, and Weiss [7] have identified the homotopy type of the classifying space of the cobordism category with objects (d −1)-dimensional manifolds embedded in ℝ ∞ . In this paper we apply the techniques of spaces of manifolds, as developed by the author and Galatius in [8], to identify the homotopy type of the cobordism category with objects (d −1)-dimensional submanifolds of a fixed background manifold M. There is a description in terms of a space of sections of a bundle over M associated to its tangent bundle. This can be interpreted as a form of Poincare duality, relating a space of submanifolds of M to a space of functions on M.
Moduli spaces of G2 manifolds

This paper is a review of current developments in the study of moduli spaces of G2 manifolds. G2 manifolds are 7-dimensional manifolds with the exceptional holonomy group G2. Although they are odd-dimensional, in many ways they can be considered as an analogue of Calabi-Yau manifolds in 7 dimensions. They play an important role in physics as natural candidates for supersymmetric vacuum solutions of M-theory compactifications. Despite the physical motivation, many of the results are of purely mathematical interest. Here we cover the basics of G2 manifolds, local deformation theory of G2 structures and the local geometry of the moduli spaces of G2 structures.
Masters Thesis: Improved Fast Inverse Nonlinear Fourier Transform for Multi-solitons

The relation between the input of an ideal optical single-mode fiber and the corresponding fiber output constitutes a nonlinear system that can be described using the nonlinear Schrödinger equation. This nonlinear system has the interesting property that it can be solved analytically using nonlinear Fourier transforms. To utilize this property, new methods of optical communication are being developed by embedding information in the nonlinear Fourier domain and employing fast nonlinear Fourier transforms. Many of the recent works use a specialized form of inverse nonlinear Fourier transform to generate information-bearing fiber inputs in the form of so-called multi-soliton pulses. Recently, multiple fast inverse nonlinear Fourier transform algorithms that can generate multi-solitons have been proposed. The goal of this thesis is to study and improve these algorithms, in particular, with respect to their computational complexity. Based on the literature survey, discrete Darboux transform combined with other discrete techniques is studied and a new algorithm is proposed. The algorithm employs a single-start approach in which discrete Darboux matrix is computed at only one sample point and rest of the samples are computed by evolution of the Darboux matrix. The algorithm is hence named as discrete Darboux evolution algorithm (DDE). The errors in the generated signal and run-time are studied by comparison with the classical Darboux transform (CDT). The DDE algorithm is shown to have floating point operations complexity of O(KN) for K eigenvalues and N samples. However, in a limited precision environment the number of samples that can be generated is found to be limited. To better understand the effects of machine precision, both the CDT and DDE algorithms are studied in a multi-precision environment. Certain insights from the study are used to develop two modifications to overcome the limitations. The first modification computes the signal using multiple single-start runs while the second one uses a multi-start approach. The second modification is shown to have errors comparable with other fast algorithms in literature. Additionally, in a qualitative comparison it is shown to be potentially faster than existing algorithms in a certain regime. Master of Science Thesis Shrinivas Chimmalgi
Spreading speeds in reducible multitype branching random walk

This paper gives conditions for the rightmost particle in the $n$th generation of a multitype branching random walk to have a speed, in the sense that its location divided by n converges to a constant as n goes to infinity. Furthermore, a formula for the speed is obtained in terms of the reproduction laws. The case where the collection of types is irreducible was treated long ago. In addition, the asymptotic behavior of the number in the nth generation to the right of na is obtained. The initial motive for considering the reducible case was results for a deterministic spatial population model with several types of individual discussed by Weinberger, Lewis and Li [J. Math. Biol. 55 (2007) 207-222]: the speed identified here for the branching random walk corresponds to an upper bound for the speed identified there for the deterministic model.
Maximal r-Diameter Sets and Solids of Constant Width

We recall the definition of an r-maximal set in a metric space as a maximal subset of diameter r. In the special case when the metric space is Euclidean such a set is exactly a solid of constant diameter r. In the process of reviewing the theory of these objects we provide a simple construction which generates a large class of such solids.
Cell fate of Müller cells during photoreceptor regeneration in an MNU-induced retinal degeneration model of zebrafish

Zebrafish can regenerate several organs such as the tail fin, heart, central nervous system, and photoreceptors. Very recently, a study has demonstrated the photoreceptor regeneration in the alkylating agent N -methyl- N -nitrosourea (MNU)-induced retinal degeneration (RD) zebrafish model, in which whole photoreceptors are lost within a week after MNU treatment and then regenerated within a month. The research has also shown massive proliferation of Müller cells within a week. To address the question of whether proliferating Müller cells are the source of regenerating photoreceptors, which remains unknown in the MNU-induced zebrafish RD model, we employed a BrdU pulse-chase technique to label the proliferating cells within a week after MNU treatment. As a result of the BrdU pulse-chase technique, a number of BrdU + cells were observed in the outer nuclear layer as well as the inner nuclear layer. This implies that regenerating photoreceptors are derived from proliferating Müller cells in the zebrafish MNU-induced RD model.
A Reference-Free Debonding Monitoring Technique in CFRP Strengthened RC Structures Using Active Sensing Materials

This study proposes a new concept of real-time nondestructive testing (NDT) for debonding monitoring, which continuously inspects the bonding condition between carbon fiber-reinforced polymer (CFRP) and host reinforced concrete (RC) structures. The uniqueness of this new NDT concept is in detecting debonding without relying on previously-obtained baseline data . The proposed reference-free damage diagnosis is achieved based on the concept of time reversal acoustics (TRA). According to TRA, an input signal at an excitation point can be reconstructed if the response signal measured at another point is reemitted to the original excitation point after being reversed in the time domain. A nonlinear damage along the wave propagation path generates the deviation of the reconstructed signal from the known initial input signal. This discrepancy of the two signals allows instantaneous identification of damage without requiring a baseline signal representing the undamaged state for comparison. The concept of TRA has been extended to guided-wave propagation within the CFRP-strengthened RC beams to improve the detectability of local debonding. Monotonic and fatigue load tests of large-scale CFRP-strengthened RC beams are conducted to demonstrate the potential of the proposed reference-free debonding monitoring system. a host reinforced concrete structure is developed. The uniqueness of this study is in developing a new concept and theoretical framework of nondestructive testing (NDT), in which debonding is detected without using previously obtained baseline data . The potential of the proposed method is demonstrated using experimental data obtained from three loading tests of two CFRP strengthened RC beams: a monotonic load test (Case I), a fatigue load test (Case II), and a monotonic test following the fatigue load test (Case III). The proposed approach successfully estimated the initiation and region of debonding. The experimental results demonstrate the potential advantage of adopting the time reversal process for damage diagnosis over conventional approaches: It is expected that the proposed reference-free NDT technique is suitable for field deployment and is particularly effective in minimizing false-positive indications of defects. In addition, the proposed approach is able to sense over a larger area for debonding monitoring than conventional strain gauges or impedance measurements, which provide only discrete points or near-field measurements.
A new decade for social changes

This paper applies the Kuznets (1955) curve approach to road traffic crashes in Algeria based on active population, motorization rate, income per capita, and land artificialization. It aims to establish a link between economic development and road safety by estimating the terms of quadratic equations related to the occurrence of traffic collisions. The results reveal that a link between economic development and road safety can be validated by two econometric specifications for the Kuznets curve (KC). Indeed, because economic conditions remained favorable, the Algerian economy reached its inflection point in 2011 and then entered the second phase of the KC. The increase in the level of economic development then in turn led to an improved road-safety situation in terms of lower mortality rates on the roads.
Opuntia dillenii: A Forgotten Plant with Promising Pharmacological Properties

Generative and vegetative parts of the cactuses have had a long-lasting position in folk medicine and their effects could partly be confirmed in scientific experiments. Nowadays, the cactus, fruits, and cladodes are the focus of many studies because of their desirable properties. Therefore, the summarized reports of valuable properties of medicinal plants may be a good way to familiarize researches with a new source of drugs with lower side effects and higher efficacy. Opuntia dillenii, a well-known member of the Cactaceae family, is used as a medicinal plant in various countries and grows in the desert, semi-desert, tropical and sub-tropical areas. It shows diverse pharmacological activities such as: antioxidant, anti-inflammatory, anti-tumor, neuroprotective, hepatoprotective, hypotensive etc. OD fruit also possesses valuable constitutes for instance: betalains, ascorbic acid, total phenol, protein as well as essential elements which suggest the significant potential of this plant as a complementary therapy against several pathological conditions. This review describes experimental evidence about pharmacological and therapeutic potential of OD in order to give the basis of its application in the prevention and treatment of some chronic diseases. More studies on OD can help better understanding of its pharmacological mechanism of action to explain its traditional uses and to identify its potential new therapeutic applications.
Combinatorial rigidity of 3-dimensional simplicial polytopes

A simplicial polytope is combinatorially rigid if its combinatorial structure is determined by its graded Betti numbers which are important invariant coming from combinatorial commutative algebra. We find a necessary condition to be combinatorially rigid for 3-dimensional reducible simplicial polytopes and provide some rigid reducible simplicial polytopes.
Generalization and Geometrization of the Kowalevski top

A new view on the Kowalevski top and the Kowalevski integration procedure is presented. For more than a century, the Kowalevski 1889 case, attracts full attention of a wide community as the highlight of the classical theory of integrable systems. Despite hundreds of papers on the subject, the Kowalevski integration is still understood as a magic recipe, an unbelievable sequence of skilful tricks, unexpected identities and smart changes of variables. The novelty of our present approach is based on our four observations. The first one is that the so-called fundamental Kowalevski equation is an instance of a pencil equation of the theory of conics which leads us to a new geometric interpretation of the Kowalevski variables $w, x_1, x_2$ as the pencil parameter and the Darboux coordinates, respectively. The second is observation of the key algebraic property of the pencil equation which is followed by introduction and study of a new class of {\bf discriminantly separable polynomials}. All steps of the Kowalevski integration procedure are now derived as easy and transparent logical consequences of our theory of discriminantly separable polynomials. The third observation connects the Kowalevski integration and the pencil equation with the theory of multi-valued groups. The Kowalevski change of variables is now recognized as an example of a two-valued group operation and its action. The final observation is surprising equivalence of the associativity of the two-valued group operation and its action to $n=3$ case of the Great Poncelet Theorem for pencils of conics.