Miracle-dz/UniFAR-FTUs huggingface dataset:
Some results concerning the representation theory of the algebra underlying loop quantum gravity

Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of (kinematical) observables and of a representation of A on a measure space over the space of generalized connections. This representation is singled out by its elegance and diffeomorphism covariance. Recently, in the context of the quest for semiclassical states, states of the theory in which the quantum gravitational field is close to some classical geometry, it was realized that it might also be worthwhile to study different representations of the algebra A. The content of the present work is the observation that under some mild assumptions, the mathematical structure of representations of A can be analyzed rather effortlessly, to a certain extent: each representation can be labeled by sets of functions and measures on the space of (generalized) connections that fulfill certain conditions.
Diagnostic performance of mono-exponential DWI versus diffusion kurtosis imaging in breast lesions: A meta-analysis

Background: This meta-analysis aimed to explore the diagnostic value of diffusion kurtosis imaging (DKI) compared to mono-exponential diffusion weighted imaging (DWI) in the diagnosis of breast cancer. Methods: A systematic electronic literature search (up to September 2020) was conducted for published English-language studies comparing the diagnostic values of DKI and DWI for the detection of breast cancer. The data of mean kurtosis (MK), mean diffusivity (MD), and apparent diffusion coefficient (ADC) were extracted to construct 2 × 2 contingency tables. The pooled sensitivities, specificities, and areas under the receiver operating characteristic curve (AUCs) were compared between DKI and DWI in the diagnosis of breast cancer. Results: Eight studies were finally included, with a total of 771 patients in the same population. Pooled sensitivities were 82.0% [95% confidence interval (95% CI), 78.2‐85.3%] for ADC, 87.3% (95% CI, 83.9‐90.1%) for MK, and 83.9% (95% CI, 80.2‐87.1%) for MD. Pooled specificities were 81.1% (95% CI, 76.7‐84.9%) for ADC, 85.1% (95% CI, 81.1‐88.5%) for MK, and 83.2% (95% CI, 79.0‐86.8%) for MD. According to the summary receiver operator characteristic curve analyses, the AUCwas 0.901 for ADC, 0.930 for MK, and 0.918 for MD (ADC vs MK, P = .353; ADC vs MD, P = .611). No notable publication bias was found, while significant heterogeneity was observed. Conclusions: Although DKI is feasible for identifying breast cancer, MD and MK offer similar diagnostic performance to ADC values. Thus, we recommend that DKI should not be included in the routine evaluation of breast lesions now.
Eplett's theorem for self-converse generalised tournaments

The converse of a tournament is obtained by reversing all arcs. If a tournament is isomorphic to its converse, it is called self–converse. Eplett provided a necessary and sufficient condition for a sequence of integers to be realisable as the score sequence of a self–converse tournament. In this paper we extend this result to generalised tournaments.
Injectivity of satellite operators in knot concordance

Let P be a knot in a solid torus, K be a knot in S3 and P(K) be the satellite knot of K with pattern P . This defines an operator P:K→K on the set of knot types and induces a satellite operator P:C→C on the set of smooth concordance classes of knots. There has been considerable interest in whether certain such functions are injective. For example, it is a famous open problem whether the Whitehead double operator is weakly injective (an operator is called weakly injective if P(K)=P(0) implies K=0 where 0 is the class of the trivial knot). We prove that, modulo the smooth four‐dimensional Poincaré Conjecture, any strong winding number 1 satellite operator is injective on C . More precisely, if P has strong winding number 1 and P(K)=P(J), then K is smoothly concordant to J in S3×[0,1] equipped with a possibly exotic smooth structure. We also prove that any strong winding number 1 operator is injective on the topological knot concordance group. If P(0) is unknotted, then strong winding number 1 is the same as (ordinary) winding number 1. More generally, we show that any satellite operator with non‐zero winding number n induces an injective function on the set of Z[1/n] ‐concordance classes of knots. We deduce some analogous results for links.
Pathwise stochastic integrals and It\^o formula for multidimensional Gaussian processes

In this article we study existence of pathwise stochastic integrals with respect to a general class of $n$-dimensional Gaussian processes and a wide class of adapted integrands. More precisely, we study integrands which are functions that are of locally bounded variation with respect to all variables. Moreover, multidimensional It\^o formula is derived.
Comparing multiplier ideals to test ideals on numerically ℚ‐Gorenstein varieties

We show that the reduction to positive characteristic of the multiplier ideal in the sense of de Fernex and Hacon agrees with the test ideal for infinitely many primes, assuming that the variety is numerically Q ‐Gorenstein. It follows, in particular, that this reduction property holds in dimension 2 for all normal surfaces.
Is Tenecteplase a Viable Alternative to Alteplase in the Treatment of Acute Ischemic Stroke?

794 In 1995, the publication of the National Institute of Neurological Disorders and Stroke (NINDS) Study using the recombinant tissue plasminogen activator (t‐PA) Alteplase for the treatment of Acute Ischemic Stroke (AIS) was the beginning of a paradigm shift in the field of AIS. [1] Significant progress was made since the original NINDS t‐PA study over the next two decades in the treatment of AIS and presently IV alteplase is recommended for selected AIS patients who can be treated within 4.5 hours of ischemic stroke symptom onset. [2] Besides, Mechanical Thrombectomy (MT) has now become the standard of care in the management of selected Large Vessel Occlusion (LVO) AIS patients when MT can be initiated within 6 hours from symptoms onset and in a very few select AIS patients where MT can be initiated within 24 hours of stroke onset. [2] However, some challenges remain in the management of AIS and much more so in infrastructure and resource poor regions of the world.
Movement Disorder Emergencies: When “Too Much” or “Too Little” Movement Needs Urgent Attention!!

801 Although most patients with movement disorders (MD) present in outpatient services and are managed in ambulatory settings, there are instances when they land up in neurological emergencies, either due to a rapidly appearing new MD or acute exacerbation of a chronic MD. [1] MD emergencies (MDEs) include acute or subacute onset progressive neurological disorders having MD as their predominant manifestation, with a likelihood of significant morbidity or mortality if not managed urgently. [2] Based on the predominant MD phenomenology, they can be classified into either hyperkinetic or hypokinetic MDEs. [3,4] While chorea, ballism, dystonia, tremor, myoclonus, and tics comprise the hyperkinetic group, acute parkinsonism, neurolept malignant syndrome (NMS), serotonin syndrome (SS), and malignant catatonia are the major hypokinetic MDEs. [3,4] Larger studies evaluating MDEs are lacking, and most of the literature consists of case reports or case series.
The evolution of K* and the halo occupation distribution since z= 1.5: observations versus simulations

We study the evolution of the K-band luminosity function (LF) and the halo occupation distribution (HOD) using Subaru observations of 15 X-ray clusters at z= 0.8-1.5 and compare the results with mock clusters (0 <z <1.3) extracted from the Millennium Simulation and populated with galaxies by means of the semi-analytic model (SAM) of Bower et al., matched in mass to our observed sample. By fixing the faint-end slope (α=-0.9), we find that the characteristic luminosity K* defined by a Shechter LF is consistent with the predictions of the SAM, which are found, for the first time, to mimic well the evolution of K* in rich clusters at z≥ 1. However, we cannot distinguish between this model and a simple stellar population synthesis model invoking passive evolution with a formation redshift (z f≃ 5) - consistent with the presence of an old red galaxy population ubiquitous in rich clusters at z= 1.5. We also see a small difference (ΔK*≃ 0.5) between our clusters and studies of the field population at similar redshifts, which suggests only a weak dependence of the luminous (L≥L*) part of the LF on cluster environment. Turning to our study of the HOD, we find that within a radius corresponding to a density 500 times critical, high-z clusters tend to host smaller numbers of galaxies to a magnitude K*+ 2 compared to their low-z counterparts. This behaviour is also seen in the mock samples and is relatively insensitive to the average mass of the cluster haloes. In particular, we find significant correlations of the observed number of member cluster galaxies (N) with both z and cluster mass: Finally, we examine the spatial distribution of galaxies and provide a new estimate of the concentration parameter for clusters at high redshift (). Our result is consistent with predictions from both our SAM mock clusters and predictions of dark matter haloes from the literature. The mock sample predictions rise slowly with decreasing redshift reaching at z= 0.
Effect of cataract surgery on the progression of age-related macular degeneration

Background: Cataracts and age-related macular degeneration (AMD) are common causes of decreased vision and blindness in individuals over age 50. Although surgery is the most effective treatment for cataracts, it may accelerate the progression of AMD, so this study further evaluated the influence of cataract surgery for AMD through a systematic review and meta-analysis. Methods: The Cochrane Systematic Evaluation method was adopted, and computer searches were conducted for the China Knowledge Network, Wanfang, Vipul, SinoMed, PubMed, SpringerLink, Clinicalkey, Medline, Cochrane Library, Web of Science, OVID, and Embase databases of cohort studies on the impact of cataract surgery on AMD, with search timeframes up to May 2022. Meta-analysis was performed using Stata/12.0. Results: A total of 8 cohort studies were included in the study. The results showed that the relative risk (RR) of AMD progression after cataract surgery was not significantly different, RR 1.194 [95% credibility interval (CI) 0.897‐1.591]; the risk remained increased more than 5 years after surgery, RR 1.372 (95% CI 1.062‐1.772). Conclusion: There is still a significant positive correlation between cataract surgery and increase the risk of worsening of AMD progression, and faster progression of early-to-late AMD found in cataract surgery with longer follow-up of patients.
Abelian surfaces with odd bilevel structure

Abelian surfaces with weak bilevel structure were introduced by S. Mukai in [14]. There is a coarse moduli space, denoted Abil t , for abelian surfaces of type (1, t) with weak bilevel structure. Abil t is a Siegel modular threefold, and can be compactified in a standard way by Mumford’s toroidal method [1]. We denote the toroidal compactification (in this situation also known as the Igusa compactification) by Abil∗ t . It is a projective variety over C, and it is shown in [14] that Abil∗ t is rational for t ≤ 5. In this paper we examine the Kodaira dimension κ(Abil∗ t ) for larger t. Our main result is the following (Theorem VIII.1).
Prevalence of Hepatitis B infections and associated risk factors among pregnant women at Hawa Memorial Saviour Hospital in the Abuakwa North Municipality, Ghana

Background : Hepatitis B virus infection is one of the most common public health problems worldwide. Over one million people globally are estimated to die annually of virus-related chronic liver disease. The routes of transmission include perinatal transmission at birth, unprotected sexual intercourse, injecting drugs, contaminated blood, and blood products, and through medical practices. In Ghana, there is a paucity of information about the prevalence of the Hepatitis B virus, its risk factors, knowledge, attitude, and practices among the population including pregnant women who are at higher risk of the infection. Methodology : This was a cross-sectional study conducted among a sample of 260 systematically selected pregnant women attending an Antenatal Clinic at Hawa Memorial Saviour Hospital in the Abuakwa North Municipality of the Eastern Region of Ghana. Demographic characteristics, risk factors, and respondents’ perceived knowledge, attitudes and practices on the disease were evaluated using a standardized structured questionnaire. Blood samples of participants were taken to determine their Hepatitis B seroprevalence using the HBV detection kit set device after the questionnaires were administered. Descriptive statistics were used to report on variables of key, while a Person’s Chi-Square test was employed to determine the association between selected variables and an outcome variable. Results : The seropositivity of Hepatitis B among pregnant women was 4.6% which is an intermediate endemicity. The majority of the study participants were between the age group 30-34years (35.38%). However, the study found that the infection rate was highest among age groups 20-24years (12%). The sociodemographic characteristics of the respondents in the study showed that only marital status (p< 0.05) was significantly associated with Hepatitis B infection. There was inadequate knowledge among respondents which was largely due to a low level of education on Hepatitis B infection at the Antenatal clinic of the Hospital. The study also found that respondents that are categorized as having low-risk levels had a seropositivity rate of 5.3% which is higher than the overall seropositivity rate of the study, and even though most people had good practices, Hepatitis B infection was highly prevalent among them. Conclusions : The study showed that Hepatitis B virus infection was highest (12%) among the age groups of 20-24 years. Only the respondents’ marital status (p<0.05) was noted to be significantly associated with infection. The detected inadequate knowledge, attitudes, and practices in the transmission and prevention of the disease call for full attention to the risk factor among respondents in the development of relevant policies and public health programs to address this important public health problem.
Stokes' theorem, volume growth and parabolicity

We present some new Stokes' type theorems on complete non-compact manifolds that extend, in different directions, previous work by Gaffney and Karp and also the so called Kelvin-Nevanlinna-Royden criterion for (p-)parabolicity. Applications to comparison and uniqueness results involving the p-Laplacian are deduced.
Geometric structures of late points of a two-dimensional simple random walk

We consider the problem, as suggested by Dembo ($2003$, $2006$), of late points of a simple random walk in two dimensions. It has been shown that the exponents for the numbers of pairs of late points coincide with those of nearly favorite points and high points in the Gaussian free field, whose exact values are known. We estimate the exponents for the numbers of a multipoint set of late points in average. While there have been observed certain similarities between among three classes of points, our results exhibit a difference.
The slow regime of randomly biased walks on trees

We are interested in the randomly biased random walk on the supercritical Galton--Watson tree. Our attention is focused on a slow regime when the biased random walk $(X_n)$ is null recurrent, making a maximal displacement of order of magnitude $(\log n)^3$ in the first $n$ steps. We study the localization problem of $X_n$ and prove that the quenched law of $X_n$ can be approximated by a certain invariant probability depending on $n$ and the random environment. As a consequence, we establish that upon the survival of the system, $\frac{|X_n|}{(\log n)^2}$ converges in law to some non-degenerate limit on $(0, \infty)$ whose law is explicitly computed.
A RETROSPECTIVE STUDY OF COMMON POULTRY DISEASES AT GAZIPUR DISTRICT OF BANGLADESH

This study was performed to investigate the prevalence of various diseases in poultry based on species, breed, sex and age in Gazipur district. The experimental data were recorded throughout the study period from January 2018 to March 2020. A total of 560 diseased and dead poultry (279 layer, 194 broilers, 77 sonali and 10 ducks) were considered in this study. The prevalence of diseases was investigated by the clinical signs, gross lesions in different organs and histopathological changes of different tissues. The prevalence of bacterial and viral diseases in different types of poultry was 38.2% and 27.1%, respectively. Among the different types of poultry, the highest prevalence of diseases (49.8%) was found in layer chicken. The prevalence of diseases in broiler, sonali chickens and ducks were 34.6%, 13.8% and 1.8%, respectively. In layer chickens, salmonellosis was found as most prevalent (21.5%) followed by colibacillosis (9.0%) and Newcastle disease (ND) (9.0%). In broiler and sonali chickens, salmonellosis (20.6% and 20.8%) was the most prevalent disease followed by infectious bursal disease (IBD) (17.0% and 10.4%) and colibacillosis (11.9% and 11.7%). However, duck plague (40%) was found as the most prevalent disease in ducks. Among the viral diseases, IBD was found as the most prevalent (11.3%). On the other hand, salmonellosis was the highest prevalent disease constituting 18.4% of all bacterial diseases.
Firm Market Power, Worker Mobility, and Wages in the US Labor Market

Worker mobility and wages have declined in the United States amid rising employer market power. I propose a theory of the labor market in which a decrease in employer competition, characterized by fewer firms per worker, drives the decline in worker mobility and wages. A finite and decreasing number of employers exert market power by excluding their offers from the outside options of their employees. This reduces the value of workers’ outside options and, consequently, their wages and transitions across employers. I quantify the model to explain the long-run decline in worker mobility and wages and examine its cross-sectional implications.
Hessian Formulas and Estimates for Parabolic Schrödinger Operators

We study the Hessian of the fundamental solution to the parabolic problem for weighted Schr\"odinger operators of the form $\frac 12 \Delta+\nabla h-V$ proving a second order Feynman-Kac formula and obtaining Hessian estimates. For manifolds with a pole, we use the Jacobian determinant of the exponential map to offset the volume growth of the Riemannian measure and use the semi-classical bridge as a delta measure at $y_0$ to obtain exact Gaussian estimates. These estimates are in terms of bounds on $Ric-2 Hess (h)$, on the curvature operator, and on the cyclic sum of the gradient of the Ricci tensor.
The (he)art of gluing

We introduce a notion of gluability for poset-indexed Bridgeland slicings on triangulated categories and show how a gluing abelian slicing on the heart of a bounded $t$-structure naturally induces a family of perverse $t$-structures. Our setup generalises the one of Collins and Polishchuk. As a corollary we recover several constructions from the theory of $t$-structures on triangulated categories. In particular we rediscover Levine's theorem: the Beilinson-Soul\'e vanishing conjecture implies the existence of Tate motives.
Arthur parameters and cuspidal automorphic modules of classical groups

The endoscopic classification via the stable trace formula comparison provides certain character relations between irreducible cuspidal automorphic representations of classical groups and their global Arthur parameters, which are certain automorphic representations of general linear groups. It is a question of J. Arthur and W. Schmid that asks: How to construct concrete modules for irreducible cuspidal automorphic representations of classical groups in term of their global Arthur parameters? In this paper, we formulate a general construction of concrete modules, using Bessel periods, for cuspidal automorphic representations of classical groups with generic global Arthur parameters. Then we establish the theory for orthogonal and unitary groups, based on certain well-expected conjectures. Among the consequences of the theory in this paper is that the global Gan-Gross-Prasad conjecture for those classical groups is proved in full generality in one direction and with a global assumption in the other direction.
Kaluza theory with zero-length extra dimensions

A new approach to the Kaluza theory and its relation to the gauge theory is presented. Two degenerate metrics on the 4 + d-dimensional total manifold are used, one corresponding to the spacetime metric and giving the fiber of the gauge bundle, and the other one to the metric of the fiber and giving the horizontal bundle of the connection. When combined, the two metrics give the Kaluza metric and its generalization to the non-Abelian case, justifying thus his choice. Considering the two metrics as fundamental rather than the Kaluza metric explains why Kaluza’s theory should not be regarded as five-dimensional (5D) vacuum gravity. This approach suggests that the only evidence of extra dimensions is given by the existence of the gauge forces, explaining thus why other kinds of evidence are not available. In addition, because the degenerate metric corresponding to the spacetime metric vanishes along the extra dimensions, the lengths in the extra dimensions is zero, preventing us to directly probe them. Therefore, this approach suggests that it is not justified to search for experimental evidence of the extra dimensions as if they are merely extra spacetime dimensions. On the other hand, the new approach uses a very general formalism, which can be applied to known and new generalizations of the Kaluza theory aiming to achieve more and make different experimental predictions.
Counting Links and Knots in Complete Graphs

We investigate the minimal number of links and knots in complete partite graphs. We provide exact values or bounds on the minimal number of links for all complete partite graphs with all but 4 vertices in one partition, or with 9 vertices in total. In particular, we find that the minimal number of links for $K_{4,4,1}$ is 74. We also provide exact values or bounds on the minimal number of knots for all complete partite graphs with 8 vertices.
A counterexample to a Penrose inequality conjectured by Gibbons

We show that the Brill–Lindquist initial data provide a counterexample to a Riemannian Penrose inequality with charge conjectured by Gibbons. The observation illustrates a sub-additive characteristic of the area radii for the individual connected components of an outermost horizon as a lower bound of the ADM mass.