Miracle-dz/UniFAR-FTUs huggingface dataset:
Suitability of Goat Colostrum to Produce a Fermented Yogurt-Type Product

Simple Summary Colostrum is the first milk produced by a mammal after giving birth, and it is awakening a high interest for its use as a sports supplement or nutraceutical due to its higher richness in immunoglobulins, growth factors, hormones, and antimicrobial enzymes than milk. Traditionally consumed by farmers, not much attention has been paid to its potential application in the production of dairy products. As a result of the increased use of artificial lactation in dairy goat systems, a surplus of colostrum is beginning to be found on farms, and the production of fermented milk may be a good opportunity for its use. This work focused on the study of the suitability of goat colostrum to produce a yoghurt-type product and compared its physicochemical, technological, mechanical, microbiological, and sensorial characteristics with those of milk. Results indicate that a colostrum yogurt with a high acceptability by consumers was obtained. Abstract The aim of this study was to investigate the potential use of goat colostrum to produce a yogurt-type product as a novel functional dairy food. Four batches of fermented goat colostrum (GCY) were produced using fermented goat milk (GMY) as a reference. Physicochemical, mechanical, and microbial characteristics of cold storage fermented products were evaluated in a weekly basis for 28 days. Sensory analysis was applied to detect potential differences between products and to evaluate the acceptance of GCY by consumers. Results indicate that colostrum showed higher coagulation times than goat milk (480 vs. 350 min to reach pH 4.6). In general, GCY showed a higher protein and fat content and similar features than GMY for most quality parameters, which were highly stable along time. Sensory evaluation led to significant differences between products related to their color and taste. The consumer acceptance test, using a 5 point-Likert scale, showed an overall acceptance of 3.90 ± 0.79 for GCY, with aroma and consistency being the sensory attributes having highest ratings (4.30 ± 0.80 and 4.20 ± 0.96, respectively). Therefore, fermenting goat colostrum with yogurt specific starters could be an interesting alternative to make use of surplus colostrum on farms, allowing for the diversification of commercial goat milk products with potential health benefits for the consumer.
Explosive Crump-Mode-Jagers branching processes

In this paper we initiate the theory of Crump-Mode-Jagers branching processes (BP) in the setting where no Malthusian parameter exist, i.e., the process grows faster than exponential. A Crump-Mode-Jagers BP is a branching process (in continuous time) where arbitrary dependencies are allowed between the birth-times of the children of a single individual in the population. It is however assumed that these reproduction processes are i.i. d. point processes for different individuals. This paper focuses on determining whether this branching process explodes, that is, the process reaches infinitely many individuals in finite time. We develop comparison techniques between reproduction processes. We study special cases in terms of explosivity such as age-dependent BPs, and epidemic models with contagious intervals. For this, we superimpose a random contagious interval $[I, C]$ on every individual in the BP and keep only the children with birth-times that fall in this interval of the parent. We show that the distribution of the end $C$ of the contagious interval does not matter in terms of explosion, while the distribution of $I$ does: the epidemic explodes if and only if the two age-dependent BPs with the original birth-times and birth-times $I$ explode. We finish studying some pathological examples such as birth-time distributions that are singular to the Lebesque-measure yet they produce an explosive BP with arbitrary power-law offspring distributions.
Extremal regular graphs: the case of the infinite regular tree

In this paper we study the following problem. Let $A$ be a fixed graph, and let $\hom(G,A)$ denote the number of homomorphisms from a graph $G$ to $A$. Furthermore, let $v(G)$ denote the number of vertices of $G$, and let $\mathcal{G}_d$ denote the family of $d$--regular graphs. The general problem studied in this paper is to determine $$\inf_{G\in \mathcal{G}_d}\hom(G,A)^{1/v(G)}. $$ It turns out that in many instances the infimum is not achieved by a finite graph, but a sequence of graphs with girth (i. e., length of the shortest cycle) tending to infinity. In other words, the optimization problem is solved by the infinite $d$--regular tree. We prove this type of results for the number of independent sets of bipartite graphs, evaluations of the Tutte-polynomial, Widom-Rowlinson configurations, and many more graph parameters. Our main tool will be a transformation called $2$-lift.
Compatibility complexes of overdetermined PDEs of finite type, with applications to the Killing equation

In linearized gravity, two linearized metrics are considered gauge-equivalent, , when they differ by the image of the Killing operator, . A universal (or complete) compatibility operator for K is a differential operator K1 such that and any other operator annihilating K must factor through K1. The components of K1 can be interpreted as a complete (or generating) set of local gauge-invariant observables in linearized gravity. By appealing to known results in the formal theory of overdetermined PDEs and basic notions from homological algebra, we solve the problem of constructing the Killing compatibility operator K1 on an arbitrary background geometry, as well as of extending it to a full compatibility complex Ki (), meaning that for each Ki the operator Ki+1 is its universal compatibility operator. Our solution is practical enough that we apply it explicitly in two examples, giving the first construction of full compatibility complexes for the Killing operator on these geometries. The first example consists of the cosmological FLRW spacetimes, in any dimension. The second consists of a generalization of the Schwarzschild–Tangherlini black hole spacetimes, also in any dimension. The generalization allows an arbitrary cosmological constant and the replacement of spherical symmetry by planar or pseudo-spherical symmetry.
Improving The Efficiency Of Vesa-2 To Maximize The Energy Utilization

: Kemplang is a crunchy traditional snack of the common people in Palembang, South Sumatra, Indonesia. Normally, it roasted on an open charcoal furnace, where the smoke, the heat and the combustion gases spread out in all directions. Vertical Energy Saver (VESA) is an equipment that has already patented created to accomodate the heat, the gas, fly ash and particulate matters from charcoal furnace used for roasting and preheating the kemplang in VESA and dispose the residual heat and gases to a place that is safe for humans breath. VESA-2 is a VESA that already developed due to improve the effectiveness and the efficiency of equipment. The air flew from the bottom of VESA-2 through the charcoal furnace to the top by a suction fan. VESA-2 is still developed and improved. It is completely work on the base of forced convection. Some tests are carried out to improve performance and the energy efficiency of equipment. The results of tests conducted on the base of enlargement the volume of VESA-2 is presented here. All measurements are carried out at no load. Test results show that the energy efficiency of original VESA-2 is 20.61%, the energy efficiency of VESA-2 with 30 centimeters height addition is 27.05% and the energy efficiency of VESA-2 with height addition and 28% of cross section area enlargement is 28.18%. The height addition and the cross section area enlargement are significantly increase the energy efficiency of VESA-2.
On some linear parabolic PDEs on moving hypersurfaces

We consider existence and uniqueness for several examples of linear parabolic equations formulated on moving hypersurfaces. Specifically, we study in turn a surface heat equation, an equation posed on a bulk domain, a novel coupled bulk-surface system and an equation with a dynamic boundary condition. In order to prove the well-posedness, we make use of an abstract framework presented in a recent work by the authors which dealt with the formulation and well-posedness of linear parabolic equations on arbitrary evolving Hilbert spaces. Here, after recalling all of the necessary concepts and theorems, we show that the abstract framework can applied to the case of evolving (or moving) hypersurfaces, and then we demonstrate the utility of the framework to the aforementioned problems.
Time Dynamics of the Down-Coupling Phenomenon in 3-D NAND Strings

We present a detailed analysis of the time dynamics of the down-coupling phenomenon (DCP) in 3-D NAND Flash memory strings. The transient time dynamics of the channel potential following the wordline (WL) bias transition from the pass voltage to zero is studied via numerical simulation, highlighting the existence of three temporal regimes controlled by different physical processes: electron emission from traps, hole injection from the string edges followed by capture, and propagation along the string. The impact of these processes is separately studied, followed by an analysis of the dependence of the DCP recovery time on architectural parameters. Results highlight the relevant physics and can be used as a design guideline for NAND strings with reduced sensitivity to the DCP.
On corner avoidance of $\boldsymbol \beta$-adic Halton sequences

We consider the corner avoiding property of $s$-dimensional $\boldsymbol \beta$-adic Halton sequences. After extending this class of point sequences in an intuitive way, we show that the hyperbolic distance between each element of the sequence and the closest corner of $[0,1)^s$ is $\mathcal{O}\left(\frac{1}{N^{s/2+\epsilon}}\right)$, where $N$ denotes the index of the element. In our proof we use tools from Diophantine analysis, more precisely, we apply Schmidt's Subspace Theorem.
Extracting signatures of quantum criticality in the finite-temperature behavior of many-body systems

We face the problem of detecting and featuring footprints of quantum criticality in the finite-temperature behavior of quantum many-body systems. Our strategy is that of comparing the phase diagram of a system displaying a $T=0$ quantum phase transition with that of its classical limit, in order to single out the genuinely quantum effects. To this aim, we consider the one-dimensional Ising model in a transverse field: while the quantum $S=1∕2$ Ising chain is exactly solvable and extensively studied, results for the classical limit $(S\ensuremath{\rightarrow}\ensuremath{\infty})$ of such model are lacking, and we supply them here. They are obtained numerically, via the transfer-matrix method, and their asymptotic low-temperature behavior is also derived analytically by self-consistent spin-wave theory. We draw the classical phase diagram according to the same procedure followed in the quantum analysis, and the two phase diagrams are found unexpectedly similar: Three regimes are detected also in the classical case, each characterized by a functional dependence of the correlation length on temperature and field analogous to that of the quantum model. What discriminates the classical from the quantum case are the different values of the exponents entering such dependencies, a consequence of the different nature of zero-temperature quantum fluctuations with respect to the thermal ones.
Planar coincidences for N‐fold symmetry

The coincidence problem for planar patterns with N‐fold symmetry is considered. For the N‐fold symmetric module with N<46, all isometries of the plane are classified that result in coincidences of finite index. This is done by reformulating the problem in terms of algebraic number fields and using prime factorization. The more complicated case N≥46 is briefly discussed and N=46 is described explicitly. The results of the coincidence problem also solve the problem of colour lattices in two dimensions and its natural generalization to colour modules.
The Central Limit Theorem for Linear Eigenvalue Statistics of the Sum of Independent Matrices of Rank One

We consider $n\times n$ random matrices $M_{n}=\sum_{\alpha =1}^{m}{\tau _{\alpha }}\mathbf{y}_{\alpha }\otimes \mathbf{y}_{\alpha }$, where $\tau _{\alpha }\in \mathbb{R}$, $\{\mathbf{y}_{\alpha }\}_{\alpha =1}^{m}$ are i.i. d. isotropic random vectors of $\mathbb{R}^n$, whose components are not necessarily independent. It was shown in arXiv:0710.1346 that if $m,n\rightarrow \infty$, $m/n\rightarrow c\in \lbrack 0,\infty )$, the Normalized Counting Measures of $\{\tau _{\alpha }\}_{\alpha =1}^{m}$ converge weakly and $\{\mathbf{y}_\alpha\}_{\alpha=1}^m$ are \textit{good} (see corresponding definition), then the Normalized Counting Measures of eigenvalues of $M_{n}$ converge weakly in probability to a non-random limit found in \cite{Ma-Pa:67}. In this paper we indicate a subclass of good vectors, which we call \textit{very good} and for which the linear eigenvalue statistics of the corresponding matrices converge in distribution to the Gaussian law, i.e., the Central Limit Theorem is valid. An important example of good vectors, studied in arXiv:0710.1346 are the vectors with log-concave distribution. We discuss the conditions for them, guaranteeing the validity of the Central Limit Theorem for linear eigenvalue statistics of corresponding matrices.
Integrable Hamiltonians with D(Dn) symmetry from the Fateev–Zamolodchikov model

A special case of the Fateev–Zamolodchikov model is studied, resulting in a solution of the Yang–Baxter equation with two spectral parameters. Integrable models from this solution are shown to have the symmetry of the Drinfeld double of a dihedral group. Viewing this solution as a descendant of the zero-field six-vertex model allows for the construction of functional relations and Bethe ansatz equations.
The Role of Sleep Patterns from Childhood to Adolescence in Vigilant Attention

Only a few studies addressed age-related changes from childhood to adolescence in sleep patterns, sleepiness, and attention. Vigilant attention plays a key role in cognitive performance. While its nature and course have been investigated broadly among adults, only limited research has been conducted on its development between childhood and adolescence. The main aim of the current study was to replicate previous findings about the effects of sleep loss on age-related changes in vigilance attention performance and sleepiness in a natural setting. A total of 104 children and adolescents (46 children aged 6–9 and 58 adolescents aged 13–19) wore an actigraph for a continuous five to seven nights, including weekdays and weekends. Subjective sleepiness (Karolinska Sleepiness Scale) and a Psychomotor Vigilance Test (PVT-B) were measured on two school days and one non-school day. Findings showed that PVT-B performance differed by age group, with adolescents outperforming children in PVT-B measures in spite of their elevated subjective sleepiness. Adolescents demonstrated less sleep time and increased sleepiness. Although PVT-B performance was better among adolescents, a within-subject analysis revealed that adolescents performed better on PVT measures on weekends than on weekdays. The results are discussed in relation to the synaptic elimination model.
Curves in Lorentz-Minkowski plane with curvature depending on their position

Motivated by the classical Euler elastic curves, David A. Singer posed in 1999 the problem of determining a plane curve whose curvature is given in terms of its position. We propound the same question in Lorentz-Minkowski plane, focusing on spacelike and timelike curves. In this article, we study those curves in $\mathbb{L}^2$ whose curvature depends on the Lorentzian pseudodistance from the origin, and those ones whose curvature depends on the Lorentzian pseudodistance through the horizontal or vertical geodesic to a fixed lightlike geodesic. Making use of the notions of geometric angular momentum (with respect to the origin) and geometric linear momentum (with respect to the fixed lightlike geodesic) respectively, we get two abstract integrability results to determine such curves through quadratures. In this way, we find out several new families of Lorentzian spiral, special elastic and grim-reaper curves whose intrinsic equations are expressed in terms of elementary functions. In addition, we provide uniqueness results for the generatrix curve of the Enneper's surface of second kind and for Lorentzian versions of some well known curves in the Euclidean setting, like the Bernoulli lemniscate, the cardioid, the sinusoidal spirals and some non-degenerate conics. We are able to get arc-length parametrizations of them and they are depicted graphically.
Weak density of orbit equivalence classes and free products of infinite abelian groups

<p>We show that if a countable group <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the free product of infinite abelian groups, then for every free, probability-measure-preserving (p.m.p.) action of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, its orbit equivalence class is weakly dense in the space of p.m. p. actions of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. This extends Lewis Bowen’s result for free groups. </p>
Integration of network pharmacology and molecular docking to explore the molecular mechanism of Cordycepin in the treatment of Alzheimer’s disease

Background Cordycepin is a nucleoside adenosine analog and an active ingredient isolated from the liquid fermentation of Cordyceps. This study sought to explore the mechanism underlying the therapeutic effect of Cordycepin against Alzheimer’s disease using network pharmacology and molecular docking technology. Methods TCMSP, SYMMAP, CTD, Super-pred, SEA, GeneCards, DisGeNET database, and STRING platform were used to screen and construct the target and protein interaction network of Cordycepin for Alzheimer’s disease. The results of Gene Ontology annotation and KEGG pathway enrichment analysis were obtained based on the DAVID database. The Omicshare database was also applied in GO and KEGG pathway enrichment analysis of the key targets. The protein–protein interaction network was constructed using the STRING database, and the potential effective targets for AD were screened based on the degree values. The correlation between the potential targets of Cordycepin in the treatment of AD and APP, MAPT, and PSEN2 was analyzed using (GEPIA) databases. We obtained potential targets related to aging using the Aging Altas database. Molecular docking analysis was performed by AutoDock Vina and Pymol software. Finally, we validated the significant therapeutic targets in the Gene Expression Omnibus (GEO) database. Results A total of 74 potential targets of Cordycepin for treating Alzheimer’s disease were identified. The potential targets of Cordycepin for the treatment of AD mainly focused on Lipid and atherosclerosis (hsa05417), Platinum drug resistance (hsa01524), Apoptosis (hsa04210), and Pathways in cancer (hsa05200). Our findings suggest that the therapeutic effect of Cordycepin on AD is primarily associated with these biological processes. We obtained 12 potential therapeutic targets for AD using the degree value in Cytoscape. Interestingly, AKT1, MAPK8, BCL2L1, FOXO3, and CTNNB1 were not only significantly associated with pathogenic genes (APP, MAPT, and PSEN2) but also with longevity in Alzheimer’s Disease. Thus we speculated that the five target genes were potential core targets mediating the therapeutic effect of Cordycepin against AD. Moreover, molecular docking results analysis showed good binding affinity between Cordycepin and the five core targets. Overall, MAPK8, FOXO3 and CTNNB1 may have significant clinical and treatment implications. Conclusion Network pharmacology demonstrated that Cordycepin exerts a therapeutic effect against Alzheimer’s disease via multiple targets and signaling pathways and has huge prospects for application in treating neurodegenerative diseases.
Stability of densities for perturbed degenerate Diffusions

We study the sensitivity of the densities of some Kolmogorov like degenerate diffusion processes with respect to a perturbation of the coefficients of the non-degenerate component. Under suitable (quite sharp) assumptions we quantify how the pertubation of the SDE affects the density. Natural applications of these results appear in various fields from mathematical finance to kinetic models.
An Exploration of Prevalence and Usage of Hi-Lo Texts in Today’s Classrooms

Abstract The need for High-Interest Low-Readability books (Hi-Lo) has been acknowledged by reading specialists and teachers alike since the 1900s, yet there is a research gap regarding teacher knowledge of and access to these books. This study sought to understand teacher awareness of Hi-Lo books, access to them, and usage within classrooms in the United States. Utilizing a mixed methods survey shared via social media platforms, teachers gave their perceptions of and experiences with Hi-Lo texts. Findings point to knowledge of Hi-Lo books among teachers, but a lack of usage in the classrooms, which is influenced by stakeholders involved in curricular decision-making.
Bloch Wave Homogenization Relative to a Microstructure

In this work, we study the aspect of Bloch wave homogenization of the new notion of convergence of microstructures represented by matrices $B^\epsilon$ related to the classical $H$-convergence of $A^\epsilon$ introduced in \cite{TG-MV-1}. The new macro quantity $B^{#}$ appears to incorporate the interaction between the two microstructures $A^\epsilon,B^\epsilon$. Here we present its Bloch spectral representation along with the homogenization result.
Nonconventional moderate deviations theorems and exponential concentration inequalities

We obtain moderate deviations theorems and exponential (Bernstein type) concentration inequalities for "nonconventional" sums of the form $S_N=\sum_{n=1}^N (F(\xi_{q_1(n)},\xi_{q_2(n)},. ,\xi_{q_\ell(n)})-\bar F)$.