Miracle-dz/UniFAR-FTUs huggingface dataset:
Extremality and dynamically defined measures, part I: Diophantine properties of quasi-decaying measures

We present a new method of proving the Diophantine extremality of various dynamically defined measures, vastly expanding the class of measures known to be extremal. This generalizes and improves the celebrated theorem of Kleinbock and Margulis (’98) resolving Sprindžuk’s conjecture, as well as its extension by Kleinbock, Lindenstrauss, and Weiss (’04), hereafter abbreviated KLW. As applications we prove the extremality of all hyperbolic measures of smooth dynamical systems with sufficiently large Hausdorff dimension, of the Patterson–Sullivan measures of all nonplanar geometrically finite groups, and of the Gibbs measures (including conformal measures) of infinite iterated function systems. The key technical idea, which has led to a plethora of new applications, is a significant weakening of KLW’s sufficient conditions for extremality. In Part I, we introduce and develop a systematic account of two classes of measures, which we call quasi-decaying and weakly quasi-decaying. We prove that weak quasi-decay implies strong extremality in the matrix approximation framework, thus proving a conjecture of KLW. We also prove the “inherited exponent of irrationality” version of this theorem, describing the relationship between the Diophantine properties of certain subspaces of the space of matrices and measures supported on these subspaces. In subsequent papers, we exhibit numerous examples of quasi-decaying measures, in support of the thesis that “almost any measure from dynamics and/or fractal geometry is quasi-decaying”. We also discuss examples of non-extremal measures coming from dynamics, illustrating where the theory must halt.
A Localization of the Lévy Operators Arising in Mathematical Finances

The comparison principle and the existence of the solution of the integro-differential equation with L{\'e}vy operators, in the framework of the viscosity solution, are shown in this paper. For the one dimensional case, a detailed estimate of the H{\"o}lder continuity of solutions is presented, by localizing the singularity of the L{\'e}vy measure.
Towards a holistic view of the heating and cooling of the intracluster medium

X-ray clusters are conventionally divided into two classes: ‘cool core’ (CC) clusters and ‘non-cool core’ (NCC) clusters. Yet relatively little attention has been given to the origins of this apparent dichotomy and, in particular, to the energetics and thermal histories of the two classes. We develop a model for the entropy profiles of clusters starting from the configuration established by gravitational shock heating and radiative cooling. At large radii, gravitational heating accounts for the observed profiles and their scalings well. However, at small and intermediate radii, radiative cooling and gravitational heating cannot be combined to explain the observed profiles of either CC or NCC clusters. The inferred entropy profiles of NCC clusters require that material is ‘pre-heated’ prior to cluster collapse in order to explain the absence of low-entropy (cool) material in these systems. We show that a similar modification is also required in CC clusters in order to match their entropy profiles at intermediate radii. In CC clusters, this modification is unstable, and an additional process is required to prevent cooling below a temperature of a few keV. We show that this can be achieved by adding a self-consistent active galactic nuclei (AGN) feedback loop in which the lowest entropy, most rapidly cooling material is heated and rises buoyantly to mix with material at larger radii. The resulting model does not require fine-tuning and is in excellent agreement with a wide variety of observational data from Chandra and XMM–Newton, including entropy and gas density profiles, the luminosity–temperature relation and high-resolution spectra. The spread in cluster core morphologies is seen to arise because of the steep dependence of the central cooling time on the initial level of pre-heating. Some of the other implications of this model are briefly discussed.
An arithmetic count of the lines on a smooth cubic surface

We give an arithmetic count of the lines on a smooth cubic surface over an arbitrary field $k$, generalizing the counts that over ${\mathbf {C}}$ there are $27$ lines, and over ${\mathbf {R}}$ the number of hyperbolic lines minus the number of elliptic lines is $3$. In general, the lines are defined over a field extension $L$ and have an associated arithmetic type $\alpha$ in $L^*/(L^*)^2$. There is an equality in the Grothendieck–Witt group $\operatorname {GW}(k)$ of $k$, \[ \sum_{\text{lines}} \operatorname{Tr}_{L/k} \langle \alpha \rangle = 15 \cdot \langle 1 \rangle + 12 \cdot \langle -1 \rangle, \] where $\operatorname {Tr}_{L/k}$ denotes the trace $\operatorname {GW}(L) \to \operatorname {GW}(k)$. Taking the rank and signature recovers the results over ${\mathbf {C}}$ and ${\mathbf {R}}$. To do this, we develop an elementary theory of the Euler number in $\mathbf {A}^1$-homotopy theory for algebraic vector bundles. We expect that further arithmetic counts generalizing enumerative results in complex and real algebraic geometry can be obtained with similar methods.
Comparison of Mixed Convection in a Square Cavity with an Oscillating versus a Constant Velocity Wall

This article presents a numerical investigation of unsteady laminar mixed convection heat transfer in a two-dimensional square cavity. The cavity is configured such that one of the vertical walls is cooled and slides either with a constant speed or with a sinusoidal oscillation. A portion of the opposite stationery wall is heated by a constant temperature heat source while, the remaining walls of the cavity are thermally insulated. Different configurations of sliding wall movement and a series of Richardson numbers and Strouhal numbers are tested. The results indicate that the direction and magnitude of the sliding wall velocity affect the heat transfer rate. At low Richardson numbers, the average heat transfer rate for the cavity with an oscillating wall is found to be lower compared to that for the cavity with a constant velocity wall. In addition, at a fixed Richardson number, as the Strouhal number decreases the oscillation frequency of average Nusselt number on the vertical walls decreases; however, the oscillation amplitude of average Nusselt number increases.
The genus-one global mirror theorem for the quintic $3$ -fold

We prove the genus-one restriction of the all-genus Landau–Ginzburg/Calabi–Yau conjecture of Chiodo and Ruan, stated in terms of the geometric quantization of an explicit symplectomorphism determined by genus-zero invariants. This gives the first evidence supporting the higher-genus Landau–Ginzburg/Calabi–Yau correspondence for the quintic $3$ -fold, and exhibits the first instance of the ‘genus zero controls higher genus’ principle, in the sense of Givental’s quantization formalism, for non-semisimple cohomological field theories.
Compactifications, Hartman functions and (weak) almost periodicity

In this paper we investigate Hartman functions on a topological group $G$. Recall that $(\iota, C)$ is a group compactification of $G$ if $C$ is a compact group, $\iota: G\to C$ is a continuous group homomorphism and $\iota(G)$ is dense in $C$. A complex-valued bounded function $f$ on $G$ is a Hartman function if there exists a group compactification $(\iota, C)$ and a complex-valued bounded function $F$ on $C$ such that $f=F\circ\iota$ and $F$ is Riemann integrable, i.e. the set of discontinuities of $F$ is a null set with respect to the Haar measure. In particular we answer the question how large a compactification for a given group $G$ and a Hartman function $f$ must be, to admit a Riemann integrable representation of $f$. In order to give a systematic presentation which is self-contained to a reasonable extent, we include several separate sections on the underlying concepts such as finitely additive measures on Boolean set algebras, means on algebras of functions, integration on compact spaces, compactifications of groups and semigroups, the Riemann integral on abstract spaces, invariance of measures and means, continuous extensions of transformations and operations to compactifications, etc.
Projectional skeletons and Markushevich bases

We prove that Banach spaces with a 1‐projectional skeleton form a P ‐class and deduce that any such space admits a strong Markushevich basis. We provide several equivalent characterizations of spaces with a projectional skeleton and of spaces having a commutative one. We further analyze known examples of spaces with a noncommutative projectional skeleton and compare their behavior with the commutative case. Finally, we collect several open problems.
Evaluation of ameliorating role of avocado Persea americana fruit extract against monosodium glutamate-induced toxicity in pregnant female albino rats and their offspring

Background : Although monosodium glutamate (MSG) is commonly used as a food additive, the application of higher doses or prolonged uses significantly leads to accumulations in living cells and finally produces cellular toxicity. Persea Americana (avocado) has recently gained substantial popularity and is often marketed as a “superfood” because of its unique nutritional composition, antioxidant content, and biochemical profile . Aim : To evaluate the potential ameliorative role of avocado fruit extract against MSG-induced nephrotoxicity in pregnant rats and their offspring. Thirty-two (24 females and 8 males) albino rats were used in this study. After an acclimatization period of two weeks; the animals were mated, and the pregnant rats were randomly divided into four groups; control (G1), avocado (G2): they were supplemented with 50 mg/kg b.w. of avocado fruit extract, MSG (G3): they were given 3g / kg b.w. of MSG, every other day, and MSG &Avocado (G4): they were given an oral dose of MSG alternatively with avocado fruit extract. At the end of weaning, the female rats and their offspring were sacrificed and the blood was collected and the kidneys were excised to evaluate the renal biochemical and histopathological, and immunohistochemical investigations. Results: In MSG-treated mothers’ rats, the renal cortical sections displayed severe histopathological lesions including little renal corpuscles, atrophied glomeruli, and relatively wide Bowman ' s space. However, the offspring displayed mild renal histopathological lesions compared with their mothers. The immunohistochemical results revealed strong PCNA and Bax expression in the renal tissues of MSG-exposed mother rats and their offspring if compared with the control. Furthermore, the mean percentage value of positively expressed cells for caspase-3 appeared significantly higher in the renal cells of MSG-induced mother's rats and their offspring if compared with the control. Additionally, the levels of serum antioxidants (SOD&CAT) and potassium ions appeared significantly lowered while the level of MDA, urea, and creatinine appeared significantly higher if compared with the control. Co-supplementation of avocado fruit extract to MSG-induced mothers rats and their pups successfully alleviated the histopathological, immune-histo-chemical, apoptotic as well as biochemical changes caused by MSG. Conclusion: Avocado fruit extract has a powerful ameliorative role against MSG-induced renal toxicity in mother rats and their offspring.
Characterisation of Jhari cattle—A new cattle germplasm from Telangana

In the present study, an attempt has been made to characterize and evaluate Jhari cattle of the state. For characterization of Jhari cattle, surveys were conducted in 17 villages of 4 districts. Physical characteristics and morphometric traits were recorded for 193 animals of different age and sex. Production and reproduction performance and socio-economic parameters were recorded from 73 farmers of different villages. Animals were reared on extensive system of management, i.e. grazing only. Few farmers provided supplement feeds to the bullocks only at home during the working days. Animal houses were open with wooden stick and separated from the owner residence (82%). Jhari cattle were gray or white (90%) in body colour. Body was small, compact and in cylindrical shape. Face was convex and longer as compared to other cattle populations of the state which is the differentiating trait of Jhari cattle. Udder was not developed and mostly bowl shaped. Temperament was docile. Birth weight ranged from 12 to 18 kg in female calves and 14-24 kg in male calves. The average daily milk yield was 1.52 kg and ranged from 1.0 to 3.0 kg. Lactation length varies from 100 to 180 days with an average of 152 days. Calving interval ranged from 340 to 610 days. A pair of bullocks may plough 1 acre of land in 6-8 h. It was observed that Jhari cattle are physically distinct from the other cattle populations of the region like Kamma, Vandharvi and Thurupu. Face is the major character for differentiating with other cattle population, i.e. longer and convex type. The other differentiating characters is horns, longer and thin at the base as compared to Ongole or its grades. Keeping in view its significant contribution in livelihood of the farmers and physical traits Jhari cattle population may be registered as a distinct breed.
Influence of Pore Fluid on Grain‐Scale Interactions and Mobility of Granular Flows of Differing Volume

The presence of a pore fluid is recognized to significantly increase the mobility of saturated over dry granular flows. However, the mechanisms through which pore fluid increases mobility may not be captured in experimental flows of small volume typical of laboratory conditions. Here we present the results of dry and initially fluid saturated or “wet” experimental flows of near‐monodisperse coarse‐grained ceramic particles in a large laboratory flume for five source volumes of 0.2–1.0 m3. Measurements include flow height, velocity profile, pore pressure, and evolving solid volume fraction, as well as the final deposit shape. The dry experiments constrain the frictional properties of the common granular material and comparison with wet flows permits an independent evaluation of the interstitial fluid effects. These results demonstrate that flow dilation and strong variation in the velocity profile are directly linked to a greatly increased mobility for wet granular flows compared to dry, and a significant influence of scale as controlled by source volume on flow behavior. Excess pore pressure need not be present for these effects to occur.
Quantitative CLTs for symmetric $U$-statistics using contractions

We consider sequences of symmetric $U$-statistics, not necessarily Hoeffding-degenerate, both in a one- and multi-dimensional setting, and prove quantitative central limit theorems (CLTs) based on the use of {\it contraction operators}. Our results represent an explicit counterpart to analogous criteria that are available for sequences of random variables living on the Gaussian, Poisson or Rademacher chaoses, and are perfectly tailored for geometric applications. As a demonstration of this fact, we develop explicit bounds for subgraph counting in generalised random graphs on Euclidean spaces; special attention is devoted to the so-called `dense parameter regime' for uniformly distributed points, for which we deduce CLTs that are new even in their qualitative statement, and that substantially extend classical findings by Jammalamadaka and Janson (1986) and Bhattacharaya and Ghosh (1992).
A novel magneto-thermoelasticity theory with memory-dependent derivative

In this work, a new model of magneto-thermoelasticity theory has been constructed in the context of a new consideration of heat conduction with memory-dependent derivative. One-dimensional application for a perfect electrically conducting half-space of elastic material, which is thermally shocked, in the presence of a constant magnetic field has been solved by using Laplace transform technique. According to the numerical results and its graphs, conclusion about the new theory of magneto-thermoelasticity has been constructed and compared with dynamic classical coupled theory.
A Retrospective Study on Patient-Specific Predictors for Non-Response to Sacroiliac Joint Injections

Intra-articular or peri-articular corticosteroid injections are often used for treatment of sacroiliac joint (SIJ) pain. However, response to these injections is variable and many patients require multiple injections for sustained benefit. In this study, we aim to identify patient-specific predictors of response or non-response to SIJ injections. Identification of these predictors would allow providers to better determine what treatment would be appropriate for a patient with SIJ pain. A retrospective review of 100 consecutive patient charts spanning a 2-year period at an academic multi-specialty pain center was conducted and a multivariate regression analysis was used to identify patient-specific predictors of response to SIJ injections. Our analysis identified that a history of depression and anxiety (OR: 0.233, 95%CI: 0.057–0.954) and increased age (OR: 0.946, 95%CI: 0.910–0.984) significantly reduced the odds of responding to injections. We also found that the associated NPRS score change for SIJ injection responders was less than the minimally clinically significant value of a 2-point differential, suggesting that reported changes in pain scores may not accurately represent a patient’s perception of success after SIJ injection. These findings warrant further investigation through a prospective study and can potentially influence clinical decision making and prognosis for patients receiving SIJ injections.
T. E. Harris and branching processes

T. E. Harris was a pioneer par excellence in many fields of probability theory. In this paper, we give a brief survey of the many fundamental contributions of Harris to the theory of branching processes, starting with his doctoral work at Princeton in the late forties and culminating in his fundamental book ``The Theory of Branching Processes,'' published in 1963.
Acute child poisoning and its related risk factors during the COVID era

Background: Poisoning is an important emergency in pediatric age groups throughout the world. The causes and types of poisoning vary from place to place in the world and even within the same country, also depending upon factors such as education, demography, socioeconomic factors, customs, and local belief. Aim of this study : To determine the frequency, etiology, characteristics, clinical presentation, and outcome of acute poisoning in children presenting to the National Environmental and Clinical Toxicological Research Center (NECTR), Cairo University. Participants and Methods: The current study is a prospective cross-sectional study, conducted on 240 pediatric patients (under 18 years old) who presented with acute poisoning to National Environmental and Clinical Toxicological Research Center (NECTR), Cairo University over three months during the COVID episode. Data were statistically analyzed for; demographic data of the participating children, manner of toxicity, place of exposure, type of poison, its availability to the child, the form of poison, duration between exposure and presentation, and the first aid that may be done to the child. Also, the severity and mortality rate detected by poison severity scoring (PSS) and rate of admission to the center or ICU and outcome were analyzed. Results: The current study showed that the long stay-at-home and school absence during COVID episodes may cause an increased risk of pediatric poisoning with household poisons and medications even in educated families. Also, accidental toxicity (84.6%) is still more common than intentional toxicity (15.4%), with negligence being the most significant probable precipitating factor. The incidence significantly increased in children with educated worker fathers and in cases where only the mother is accompanying the children. In addition, the risk for ICU admission was significantly higher (51.4%) in adolescents (13 to <18 years) with intentional poisoning. Conclusion: Pediatric poisoning is an emergency condition with younger children (< 9 yrs.) are highly susceptible to accidental exposure, however, with older ages (9 to <18 years), the incidence of intentional poisoning and risk of bad outcome increases.
A New Proof for the Equivalence of Weak and Viscosity Solutions for the p-Laplace Equation

In this paper, we give a new proof for the fact that the distributional weak solutions and the viscosity solutions of the p-Laplace equation −div(|Du| p−2 Du) = 0 coincide. Our proof is more direct and transparent than the original proof of Juutinen et al. [8], which relied on the full uniqueness machinery of the theory of viscosity solutions. We establish a similar result also for the solutions of the non-homogeneous version of the p-Laplace equation.
REPRESENTATIONS OF UQ(SO(5)) AND NON-MINIMAL Q-DEFORMATION

Representations of SO(5) can be constructed on bases such that either the Chevalley triplet (e1, f1, h1) or (e2, f2, h2) has the standard SU(2) matrix elements. The other triplet in each case has a more complicated action. The q-deformation of such representations present striking differences. In one case a non-minimal deformation is found to be essential. This is explained and illustrated below. Broader interests of a parallel use of the two bases are pointed out.
Counting One-Sided Simple Closed Geodesics on Fuchsian Thrice Punctured Projective Planes

We prove that there is a true asymptotic formula for the number of one-sided simple closed curves of length $\leq L$ on any Fuchsian real projective plane with three points removed. The exponent of growth is independent of the hyperbolic metric, and it is noninteger, in contrast to counting results of Mirzakhani for simple closed curves on orientable Fuchsian surfaces.
Visual prey categorization by a generalist jumping spider

Abstract The majority of jumping spiders are visual hunters that capture a wide range of prey. While they are known to use specific predatory techniques against different prey, their prey identification mechanisms are poorly understood. A generalist jumping spider, Yllenus arenarius, employs different predatory techniques to capture prey with two different escape potentials. The aim of the present study was to identify the characteristics used by the spider to classify prey into one of these categories. Freshly-emerged spiderlings were used in the experiments to analyse pre-programmed visual predatory preferences. The spiders were presented with: a) their natural prey with different escape potentials (flies, thrips, caterpillars) and b) video images constructed from different combinations of features of their natural prey. The images varied with regard to five characteristics: body length (short vs long images), the presence or absence of details (0 or 4 details, including head spot, antennae, legs, wings), the local motion of legs (moving vs still), the type of global motion (crawling vs non-crawling) and the direction of global motion (horizontal motion vs vertical small scale jumps). Prey-specific behaviours indicated which characteristics were used by the spider to ascertain the prey’s escape potentials. Our findings indicate that during visual prey categorization, Y. arenarius can rely solely on general prey characteristics, such as body proportions and the type of prey motion, while ignoring other stimuli, such as the presence of details and the local motion of legs. This mechanism of prey identification, based on these two easily-recognizable prey characteristics, enables fairly quick and precise categorization of a wide range of prey according to their escape potentials. The study shows how generalist jumping spiders can categorize their diverse prey into a limited number of groups and discusses the presence of the mechanism in other jumping spiders and other animals.