Miracle-dz/UniFAR-FTUs huggingface dataset:
Uniform dimension results for fractional Brownian motion

Kaufman's dimension doubling theorem states that for a planar Brownian motion $\{\mathbf{B}(t): t\in [0,1]\}$ we have $$\mathbb{P}(\dim \mathbf{B}(A)=2\dim A \textrm{ for all } A\subset [0,1])=1,$$ where $\dim$ may denote both Hausdorff dimension $\dim_H$ and packing dimension $\dim_P$. The main goal of the paper is to prove similar uniform dimension results in the one-dimensional case. Let $0<\alpha<1$ and let $\{B(t): t\in [0,1]\}$ be a fractional Brownian motion of Hurst index $\alpha$. For a deterministic set $D\subset [0,1]$ consider the following statements: $$(A) \quad \mathbb{P}(\dim_H B(A)=(1/\alpha) \dim_H A \textrm{ for all } A\subset D)=1,$$ $$(B) \quad \mathbb{P}(\dim_P B(A)=(1/\alpha) \dim_P A \textrm{ for all } A\subset D)=1, $$ $$(C) \quad \mathbb{P}(\dim_P B(A)\geq (1/\alpha) \dim_H A \textrm{ for all } A\subset D)=1. $$ We introduce a new concept of dimension, the modified Assouad dimension, denoted by $\dim_{MA}$. We prove that $\dim_{MA} D\leq \alpha$ implies (A), which enables us to reprove a restriction theorem of Angel, Balka, M\'ath\'e, and Peres. We show that if $D$ is self-similar then (A) is equivalent to $\dim_{MA} D\leq \alpha$. Furthermore, if $D$ is a set defined by digit restrictions then (A) holds iff $\dim_{MA} D\leq \alpha$ or $\dim_H D=0$. The characterization of (A) remains open in general. We prove that $\dim_{MA} D\leq \alpha$ implies (B) and they are equivalent provided that $D$ is analytic. We show that (C) is equivalent to $\dim_H D\leq \alpha$. This implies that if $\dim_H D\leq \alpha$ and $\Gamma_D=\{E\subset B(D): \dim_H E=\dim_P E\}$, then $$\mathbb{P}(\dim_H (B^{-1}(E)\cap D)=\alpha \dim_H E \textrm{ for all } E\in \Gamma_D)=1. $$ In particular, all level sets of $B|_{D}$ have Hausdorff dimension zero almost surely.
Age-structured Population Models with Applications

A general model of age-structured population dynamics is developed and the fundamental properties of its solutions are analyzed. The model is a semilinear partial differential equation with a nonlinear nonlocal boundary condition. Existence, uniqueness and regularity of solutions to the model equations are proved. An intrinsic growth constant is obtained and linked to the existence and the stability of the trivial and/or the positive equilibrium. Lyapunov function is constructed to show the global stability of the trivial and/or the positive equilibrium. Key words: Lyapunov function, Partial Differential Equation, Stability, Mathematical Model, Uniform Persistence, Reproductive Number (or Reproduction Number)
Populations of OB-type stars in galaxies

Abstract One of the challenges for stellar astrophysics is to reach the point at which we can undertake reliable spectral synthesis of unresolved populations in young, star-forming galaxies at high redshift. Here I summarise recent studies of massive stars in the Galaxy and Magellanic Clouds, which span a range of metallicities commensurate with those in high-redshift systems, thus providing an excellent laboratory in which to study the role of environment on stellar evolution. I also give an overview of observations of luminous supergiants in external galaxies out to a remarkable 6.7 Mpc, in which we can exploit our understanding of stellar evolution to study the chemistry and dynamics of the host systems.
Looking for the lost torus

We classify the groups definable in the coloured fields obtained by Hrushovski amalgamation. A group definable in the bad green field is isogenous to the quotient of a subgroup of an algebraic group by a Cartesian power of the group of green elements. A definable subgroup of an algebraic group in the green or red field is an extension of the coloured points of a multiplicative or additive algebraic group by an algebraic group. In particular, a simple group in a coloured field is algebraic.
Second order optimality conditions for strong local minimizers via subgradient graphical derivative

This paper is devoted to the study of second order optimality conditions for strong local minimizers in the frameworks of unconstrained and constrained optimization problems in finite dimensions via subgradient graphical derivative. We prove that the positive definiteness of the subgradient graphical derivative of an extended-real-valued lower semicontinuous proper function at a proximal stationary point is sufficient for the quadratic growth condition. It is also a necessary condition for the latter property when the function is either subdifferentially continuous, prox-regular, twice epi-differentiable or variationally convex. By applying our results to the $\mathcal{C}^2$-cone reducible constrained programs, we establish no-gap second order optimality conditions for (strong) local minimizers under the metric subregularity constraint qualification. These results extend the classical second order optimality conditions by surpassing the well-known Robinson's constraint qualification. Our approach also highlights the interconnection between the strong metric subregularity of subdifferential and quadratic growth condition in optimization problems.
A p(x)-version of Diaz-Saa Inequality and some applications

The main result of this work is a new extension of the well known inequality by Diaz and Saa which, in our case, involves an anisotropic operator, such as the p(x)-Laplacian. Our present extension of this inequality enables us to establish several new results on the uniqueness of solutions and comparison principles for some anisotropic quasilinear elliptic equations. Our proofs take advantage of certain convexity properties of the energy functional associated with the p(x)-Laplacian.
Effects of ozonized glycerin on inflammation of mammary glands induced by intramammary lipopolysaccharide infusion in goats.

Although ozone shows antimicrobial activity against mastitis-causing pathogens in ruminants, its anti-inflammatory effect on mammary glands remains unclear. The aim of this study was to examine the anti-inflammatory effects of ozonized glycerin (OG) on experimentally induced inflammation in the mammary glands of six Shiba and two Tokara lactating goats. We infused 1 μg lipopolysaccharide (LPS) into all udders on day -1. On day 0, post LPS infusion, OG (ozone group), and glycerin (control group) were infused into the right and left sides of the udders, respectively. Milk samples were collected once daily from days -1 to 7. The somatic cell count and lactoperoxidase (LPO) activity, along with the interleukin-1β (IL-1β), tumor necrosis factor-α, IL-8, IL-10, lactoferrin, and sodium ion concentrations in milk were measured. IL-8, IL-10, and lactoferrin levels after LPS infusion in the ozone group were significantly lower than those in the control group, and the LPO activity tended to be lower than that observed in the control group. This study showed that OG has anti-inflammatory potential against LPS-induced inflammation in the mammary glands.
Regularity and Strict Positivity of Densities for the Nonlinear Stochastic Heat Equation

In this paper, we establish a necessary and sufficient condition for the existence and regularity of the density of the solution to a semilinear stochastic (fractional) heat equation with measure-valued initial conditions. Under a mild cone condition for the diffusion coefficient, we establish the smooth joint density at multiple points. The tool we use is Malliavin calculus. The main ingredient is to prove that the solutions to a related stochastic partial differential equation have negative moments of all orders. Because we cannot prove u ( t , x ) ∈ D ∞ u(t,x)\in \mathbb {D}^\infty for measure-valued initial data, we need a localized version of Malliavin calculus. Furthermore, we prove that the (joint) density is strictly positive in the interior of the support of the law, where we allow both measure-valued initial data and unbounded diffusion coefficient. The criteria introduced by Bally and Pardoux are no longer applicable for the parabolic Anderson model. We have extended their criteria to a localized version. Our general framework includes the parabolic Anderson model as a special case.
Haemosporidian parasites in the ash-breasted Sierra finch (Geospizopsis plebejus): insights from an Andean dry forest population

Abstract Abstract Haemosporidian genera Plasmodium, Haemoproteus and Leucocytozoon, responsible for avian malarial infections, are highly diverse and have a wide range of health effects and predictors, depending on the host and its environmental context. Here, we present, for the first time, detailed information on the identity, prevalence and parasitaemia of haemosporidians and other haemoparasites that infect the ash-breasted Sierra finch, Geospizopsis plebejus, in an Andean dry forest. We study the consequences of infection in the host body and health conditions and explore the environmental and intrinsic factors that influence infection status and parasitaemia. We conducted diagnoses by cytochrome b (cytb) sequencing and morphological identification, and estimated the levels of parasitaemia based on microscopy. We identified 6 cytb lineages infecting G. plebejus. Two of them were new lineages: Haemoproteus sp. GEPLE01 and GEPLE02. We also detected Haemoproteus sp. ZOCAP08, Haemoproteus sp. AMAVIR01, Plasmodium homopolare BAEBIC02 and Plasmodium cathemerium ZONCAP15. By microscopy, we detected Haemoproteus coatneyi, Haemoproteus erythrogravidus, P. homopolare and other unidentified species of Haemoproteus, Plasmodium, Babesia sp. and 1 microfilaria. We found no evidence of Leucocytozoon. Additionally, we detected several coinfections by sequencing and microscopy. The prevalence of haemosporidian infections was high (87.7%), and the mean parasitaemia was 61.65 infected cells per 10 000 erythrocytes examined. Prevalence and parasitaemia were higher for Haemoproteus than for Plasmodium. Haemoproteus sp. AMAVIR01 showed the highest prevalence (43.1%) and mean parasitaemia (94.39/10 000 erythrocytes) and might be associated with H. coatneyi. Immature individuals showed a lower prevalence than adults, supporting previous findings.
XIAP and PHB1 regulate anoikis through competitive binding to TRAF6.

Anoikis resistance is a prerequisite for circulating tumor cells to survive. However, the mechanism underlying anoikis resistance is poorly understood. In the present study, the effect of TRAF6-induced NF-kB activation on anoikis susceptibility in tumor cells was evaluated. Differential TRAF6-binding proteins in anoikis-sensitive versus anoikis-resistant tumor cells were screened by LC-MS/MS analysis. The effects of TRAF6-binding proteins on the stability of TRAF6, the activation of NF-kB signaling and anoikis susceptibility in tumor cells were detected. We found that the loss of TRAF6 expression is an important molecular event linked to anoikis. XIAP, an E3 ligase, can bind, ubiquitinate and degrade TRAF6 and may lead to inactivation of NF-κB signaling and anoikis sensitivity. High expression of PHB1 competes with XIAP for binding to TRAF6 and confers anoikis resistance to tumor cells. PHB1 and TRAF6 knockdown eliminated tumor cells from the circulation in vivo. Significant correlations between elevated PHB1 and TRAF6 expression and distant metastasis were observed in oral cancer patients. Collectively, we elucidated a novel mechanism governing anoikis. Our data also indicated that TRAF6 and PHB1 are potential therapeutic targets for tumor cells disseminating in the circulation. Implications: Our data implicate that PHB1 competes with XIAP for binding to TRAF6 and confers anoikis resistance to tumor cells.
On the Inefficiency of Forward Markets in Leader-Follower Competition

Motivated by electricity markets, this paper studies the impact of forward contracting in situations where firms have capacity constraints and heterogeneous production lead times. We consider a model with two types of firms - leaders and followers - that choose production at two different times. Followers choose productions in the second stage but can sell forward contracts in the first stage. Our main result is an explicit characterization of the equilibrium outcomes. Classic results on forward contracting suggest that it can mitigate market power in simple settings; however the results in this paper show that the impact of forward markets in this setting is delicate - forward contracting can enhance or mitigate market power. In particular, our results show that leader-follower interactions created by heterogeneous production lead times may cause forward markets to be inefficient, even when there are a large number of followers. In fact, symmetric equilibria do not necessarily exist due to differences in market power among the leaders and followers.
Assessment of genetic markers for multilocus sequence typing (MLST) of Fasciola isolates from Iran

Abstract Background Several markers have been described to characterise the population structure and genetic diversity of Fasciola species (Fasciola hepatica (F. hepatica) and Fasciola gigantica (F. gigantica). However, sequence analysis of a single genomic locus cannot provide sufficient resolution for the genetic diversity of the Fasciola parasite whose genomes are ∼1.3 GB in size. Objectives To gain a better understanding of the gene diversity of Fasciola isolates from western Iran and to identify the most informative markers as candidates for epidemiological studies, five housekeeping genes were evaluated using a multilocus sequence typing (MLST) approach. Methods MLST analysis was developed based on five genes (ND1, Pepck, Pold, Cyt b and HSP70) after genomic DNA extraction, amplification and sequencing. Nucleotide diversity and phylogeny analysis were conducted on both concatenated MLST loci and each individual locus. A median joining haplotype network was created to examine the haplotypes relationship among Fasciola isolates. Results Thirty‐three Fasciola isolates (19 F. hepatica and 14 F. gigantica) were included in the study. A total of 2971 bp was analysed for each isolate and 31 sequence types (STs) were identified among the 33 isolates (19 for F. hepatica and 14 for F. gigantica isolates). The STs produced 44 and 42 polymorphic sites and 17 and 14 haplotypes for F. hepatica and F. gigantica, respectively. Haplotype diversity was 0.982 ± 0.026 and 1.000 ± 0.027 and nucleotide diversity was 0.00200 and 0.00353 ± 0.00088 for F. hepatica and F. gigantica, respectively. There was a high degree of genetic diversity with a Simpson's index of diversity of 0.98 and 1 for F. hepatica and F. gigantica, respectively. While HSP70 and Pold haplotypes from Fasciola species were separated by one to three mutational steps, the haplotype networks of ND1 and Cyt b were more complex and numerous mutational steps were found, likely due to recombination. Conclusions Although HSP70 and Pold genes from F. gigantica were invariant over the entire region of sequence coverage, MLST was useful for investigating the phylogenetic relationship of Fasciola species. The present study also provided insight into markers more suitable for phylogenetic studies and the genetic structure of Fasciola parasites.
Radar reflector guided axillary surgery in node positive breast cancer patients

ABSTRACT Introduction In patients with non-palpable breast cancer, the availability of wireless localization techniques facilitates removal of the target lesion. One such technique uses a radar reflector for localization (RRL). This study evaluates the feasibility and effectiveness of RRL to guide excision of axillary lymph nodes in patients with node-positive breast cancer. Methods Our Breast Cancer Database was queried for patients diagnosed with breast cancer, between 5/2017 and 10/2021, who underwent preoperative placement of a radar reflector into a biopsy proven axillary lymph node. Clinicopathologic data were reported using descriptive statistics. Results Twenty patients underwent preoperative placement of a radar reflector into the axilla. Intraoperatively, the clip and radar reflector were successfully removed in all patients. Among the 10 patients treated with NAC, 5 patients achieved an axillary pathologic complete response (pCR) and were spared a complete axillary lymph node dissection (cALND). Among the entire cohort, RRL resulted in a 53% reduction in the number of lymph nodes removed. Conclusions Wireless localization of axillary lymph nodes is safe and feasible. The technique ensures excision of biopsy proven positive axillary lymph nodes and enables a targeted approach to assessing the axilla, both in the setting of NAC and upfront surgery.
Exact eigenfunctions and the open topological string

Mirror curves to toric Calabi–Yau threefolds can be quantized and lead to trace class operators on the real line. The eigenvalues of these operators are encoded in the BPS invariants of the underlying threefold, but much less is known about their eigenfunctions. In this paper, we first develop methods in spectral theory to compute these eigenfunctions. We also provide an integral matrix representation which allows them to be studied in a ’t Hooft limit, where they are described by standard topological open string amplitudes. Based on these results, we propose a conjecture for the exact eigenfunctions, which involves both the WKB wavefunction and the standard topological string wavefunction. This conjecture can be made completely explicit in the maximally supersymmetric, or self-dual case, which we work out in detail for local P1×P1. In this case, our conjectural eigenfunctions turn out to be closely related to Baker–Akhiezer functions on the mirror curve, and they are in full agreement with the first-principle calculations in spectral theory.
Products of Differences in Prime Order Finite Fields

There exists an absolute constant $C$ with the following property. Let $A \subseteq \mathbb{F}_p$ be a set in the prime order finite field with $p$ elements. Suppose that $|A| > C p^{5/8}$. The set \[ (A \pm A)(A \pm A) = \{(a_1 \pm a_2)(a_3 \pm a_4) : a_1,a_2,a_3,a_4 \in A\} \] contains at least $p/2$ elements.
LONG-PERIOD VARIATIONS IN THE RADIAL VELOCITY OF SPECTROSCOPIC BINARY M GIANT μ URSAE MAJORIS

We report that the spectroscopic binary μ Ursae Majoris (μ UMa) has secondary RV variations of 471.2 days in addition to those of 230.0 days already known. Keplerian orbit analysis yields stellar mass companions of 1.6 M⊙ for the 230 day period and 0.14 M⊙ for the 471 day period. However, the HIPPARCOS photometries show a period similar to the stellar rotational period, which is one-quarter of the RV period. Variations in the bisector velocity curvature show a period of 463.6 days. We also find ∼473 day variations in the equivalent width (EW) measurements of the H &agr; ? > and H β ? > lines, whose origin is probably stellar activity. We note that the nature of 471 day variations is similar to one observed in “Sequence D” of Asymptotic Giant Branch pulsating stars. We therefore conclude that the RV and the EW variations in the spectroscopic binary M giant μ UMa A originate from the complex pulsations and the chromospheric activity.
Subtleties of the fermion measure in the presence of axion fields

It is known from path integral studies of the chiral anomaly that the fermion measure has to depend on gauge fields interacting with the fermion. It is pointed out here that in the presence of an axion field interacting with the fermion, it too is involved in the measure, with unexpected consequences for the utility of the field.
Fast and exact evaluation of box splines via the PP-form

For the class of non-degenerate box splines, we prove that these box splines are piecewise polynomial. This is not a new result, it is in fact a well known and useful property of box splines. However, our proof is constructive, and the main result of this work is a corollary that follows from this proof, namely one that gives an explicit construction scheme for the polynomial pieces in the interior regions of any non-degenerate box spline.
A Survey of Smooth Vector Graphics: Recent Advances in Repr esentation, Creation, Rasterization, and Image Vectorization

The field of smooth vector graphics explores the representation, creation, rasterization, and automatic generation of light-weight image representations, frequently used for scalable image content. Over the past decades, several conceptual approaches on the representation of images with smooth gradients have emerged that each led to separate research threads, including the popular gradient meshes and diffusion curves. As the computational models matured, the mathematical descriptions diverged and article started to focus more narrowly on subproblems, such as on the representation and creation of vector graphics, or the automatic vectorization from raster images. Most of the work concentrated on a specific mathematical model only. With this survey, we describe the established computational models in a consistent notation to spur further knowledge transfer, leveraging the recent advances in each field. We therefore categorize vector graphics article from the last decades based on their underlying mathematical representations as well as on their contribution to the vector graphics content creation pipeline, comprising representation, creation, rasterization, and automatic image vectorization. This survey is meant as an entry point for both artists and researchers. We conclude this survey with an outlook on promising research directions and challenges to overcome in the future.
Semantics of higher inductive types

Abstract Higher inductive types are a class of type-forming rules, introduced to provide basic (and not-so-basic) homotopy-theoretic constructions in a type-theoretic style. They have proven very fruitful for the “synthetic” development of homotopy theory within type theory, as well as in formalising ordinary set-level mathematics in type theory. In this paper, we construct models of a wide range of higher inductive types in a fairly wide range of settings. We introduce the notion of cell monad with parameters: a semantically-defined scheme for specifying homotopically well-behaved notions of structure. We then show that any suitable model category has weakly stable typal initial algebras for any cell monad with parameters. When combined with the local universes construction to obtain strict stability, this specialises to give models of specific higher inductive types, including spheres, the torus, pushout types, truncations, the James construction and general localisations. Our results apply in any sufficiently nice Quillen model category, including any right proper, simplicially locally cartesian closed, simplicial Cisinski model category (such as simplicial sets) and any locally presentable locally cartesian closed category (such as sets) with its trivial model structure. In particular, any locally presentable locally cartesian closed (∞, 1)-category is presented by some model category to which our results apply.