Miracle-dz/UniFAR-FTUs huggingface dataset:
Energy forms

In this thesis we study energy forms. These are quadratic forms on the space of real-valued measurable $m$-a.e. determined functions $$E:L^0(m) \to [0,\infty],$$ which assign to a measurable function $f$ its energy $E(f)$. Their two defining characteristics are a contraction property and some form of continuity. The contraction property demands that for each normal contraction $C:\mathbb R \to \mathbb R$ the energy of a function $f$ satisfies $$E(C \circ f) \leq E(f). $$ This is an abstract formulation of the postulate that cutting off fluctuations of a function (which is thought to describe some physical quantity) decreases its energy. The continuity assumption that we impose on energy forms is lower semicontinuity with respect to local convergence in measure. We develop the basic theory of energy forms and then investigate their extensions and global properties.
Characterisation of Staphylococci Isolated from Milk Samples of a Water Buffalo Herd

Water buffalo produce a tenth of milk for global human consumption. Non-aureus staphylococci (NAS) are among the most commonly isolated bacteria from mastitis in water buffalo and dairy cows. These results described the initial characterisation of 17 NAS—15 Staphylococcus simulans and two Staphylococcus chromogenes from a water buffalo herd (n = 44) in South Africa. The isolates were identified by classical microbiology, MALDI-TOF, and 16S rRNA, and the disc diffusion method determined the antibiotic susceptibility. A multi-locus sequence typing scheme (MLST) was developed to determine S. simulans sequence types (ST), by defining and comparing seven housekeeping gene fragment sequences. Sequence typing confirmed all 15 S. simulans isolates from water buffalo which belonged to a single ST, genetically distant from the six bovine STs isolated from adjacent farms, which also varied, indicating no current bacterial transfer between species. The antibiotic resistance patterns of S. simulans varied between beta-lactams. The mean milk somatic cell count (SCC) for the water buffalo milk samples was 166,500 cells/mL milk. This information offers insights into the epidemiology and comparison among isolates from various origins, which leads to effective proactive mastitis strategies resulting in safe, high-quality dairy products from water buffalo and dairy cows for human consumption.
Levitated Micromagnets in Superconducting Traps: A New Platform for Tabletop Fundamental Physics Experiments

Magnetically levitated microparticles have been proposed as mechanical sensors with extreme sensitivity. In particular, micromagnets levitated above a superconductor can achieve very low levels of dissipation and thermal noise. In this paper, we review recent initial experiments and discuss the potential for using these systems as sensors of magnetic fields and rotational motion, as well as possible applications to fundamental physics.
Sum-avoiding sets in groups

Sum-avoiding sets in groups, Discrete Analysis 2016:15, 27 pp. Let $A$ be a subset of an Abelian group $G$. A subset $B\subset A$ is called _sum-avoiding in $A$_ if no two elements of $B$ add up to an element of $A$. Write $\phi(A)$ for the size of the largest sum-avoiding subset of $A$. If $G=\mathbb Z$ and $|A|=n$, then it is known that $\phi(A)$ must be at least $\log n(\log\log n)^{1/2-o(1)}$, and examples are known of sets for which $\phi(A)$ is at most $\exp(O(\sqrt{\log n}))$. These results are due to Xuancheng Shao and Imre Ruzsa, respectively. Reducing this gap to a reasonable size appears to be a very hard problem. If on the other hand, $G$ has torsion, then it is possible for $A$ to be large and finite while $\phi(A)$ is bounded. Indeed, if $A$ is any subgroup, then $\phi(A)=1$. However, this is not the end of the story, as the authors show. Suppose we know that $A$ is a subset of an Abelian group and that $\phi(A)\leq k$ for some fixed $k$. What can we say about $A$? Note that this condition expresses a kind of weak closure property: instead of saying that any two elements of $A$ add up to an element of $A$, it says that from any $k+1$ elements of $A$, two must add up to an element of $A$. A simple example of such a set that isn't itself a subgroup is a union of at most $k$ subgroups. Then given more than $k$ elements of $A$, two must belong to the same subgroup and hence add up to an element of $A$. In this paper, the authors show a converse to this easy observation: if $\phi(A)\leq k$, then there exist subgroups $H_1,\dots,H_m$ with $m\leq k$ such that $|A\cap H_i|\geq c|H_i|$ for each $i$, and all but at most $C$ elements of $A$ belong to $H_1\cup\dots\cup H_m$. Here, $c>0$ and $C$ are constants that depend on $k$ only. If you are familiar with the Balog-Szemeredi theorem and Freiman's theorem, then you might expect the proof of this result to be a fairly straightforward use of those tools. However, when one attempts to turn this thought into a proof, a significant difficulty arises, which the authors explain in their introduction. They resolve this difficulty by means of a complicated iterative argument -- in fact, it is sufficiently complicated that instead of desperately trying to keep control of all the parameters that would arise, they resort to the language of non-standard analysis. This tidies up the argument considerably, but at the price of yielding no bound at all for how the constants $c$ and $C$ depend on $k$. However, this is not a huge price, as they also say that if they had avoided non-standard analysis, then the bounds they would have obtained would have been extremely weak. The paper also contains a construction of arbitrarily large sets $A$ with $\phi(A)\leq k$ that contain no inverse pairs. This gives a negative answer to a question of Erdős. The construction, which is surprisingly simple, makes heavy use of the fact that their set lives in a group with order divisible by a small prime. They go on to show that this is necessary: if the order of $G$ has no small prime divisors, then Erdős's question has a positive answer.
Functorial compactification of linear spaces

We define compactifications of vector spaces which are functorial with respect to certain linear maps. These “many-body” compactifications are manifolds with corners, and the linear maps lift to b-maps in the sense of Melrose. We derive a simple criterion under which the lifted maps are in fact b-fibrations, and identify how these restrict to boundary hypersurfaces. This theory is an application of a general result on the iterated blow-up of cleanly intersecting submanifolds which extends related results in the literature.
Fast inertial dynamics and FISTA algorithms in convex optimization. Perturbation aspects

In a Hilbert space setting $\mathcal H$, we study the fast convergence properties as $t \to + \infty$ of the trajectories of the second-order differential equation $ \ddot{x}(t) + \frac{\alpha}{t} \dot{x}(t) + \nabla \Phi (x(t)) = g(t)$, where $\nabla\Phi$ is the gradient of a convex continuously differentiable function $\Phi: \mathcal H \to \mathbb R$, $\alpha$ is a positive parameter, and $g: [t_0, + \infty[ \rightarrow \mathcal H$ is a "small" perturbation term. In this damped inertial system, the viscous damping coefficient $\frac{\alpha}{t}$ vanishes asymptotically, but not too rapidly. For $\alpha \geq 3$, and $\int_{t_0}^{+\infty} t \|g(t)\| dt 3$, we show that any trajectory converges weakly to a minimizer of $\Phi$, and we show the strong convergence property in various practical situations. This complements the results obtained by Su-Boyd- Cand\`es, and Attouch-Peypouquet-Redont, in the unperturbed case $g=0$. The parallel study of the time discretized version of this system provides new insight on the effect of errors, or perturbations on Nesterov's type algorithms. We obtain fast convergence of the values, and convergence of the trajectories for a perturbed version of the variant of FISTA recently considered by Chambolle-Dossal, and Su-Boyd-Cand\`es.
Global Design of Double Protograph LDPC Codes for Joint Source-Channel Coding

In this letter, a global design of double protograph low-density parity-check (DP-LDPC) codes is proposed for joint source-channel coding (JSCC) system. The maximum number of degree-2 variable nodes (VNs), which is very important for the performance of the system, is determined from a global perspective that considers the joint protograph as a whole. Based on the allocation of degree-2 VNs, the new guidelines with this more comprehensive perspective are summarized and the global optimized DP-LDPC codes are designed. The simulation results that are in consistent with the joint protograph extrinsic information transfer (P-EXIT) analysis indicate that the optimized DP-LDPC codes have better performance compared with the existing re-designed DP-LDPC codes.
Should We Always Perform Preoperative Chest Computed Tomography in Patients with cT1a Renal Cell Carcinoma?

Simple Summary We aimed to establish an objective standard for optimal timing of preoperative chest computed tomography (CT) in patients with renal cell carcinoma (RCC). The overall rate of positive chest CT scans before nephrectomy was 3.03% (27/890). Only one patient had lung metastasis before surgery for cT1a. cT stage (≥cT1b), Charlson comorbidity index (CCI) ≥4, and low albumin/globulin ratio (AGR) were associated with a higher risk of positive chest CT scans. After 890-sample bootstrap validation, the concordance index was 0.80. The net benefit of the proposed strategy was superior to that of the select-all and select-none strategies according to decision curve analysis. Therefore, when chest CT was performed with a risk of a positive result ≥10%, 532 (59.8%) negative chest CT scans could be prevented. Only 24 (2.7%) potentially positive chest CT scans were misdiagnosed. Therefore, we recommend chest CT in patients with ≥cT1b disease, CCI ≥4, and low AGR. Abstract No definitive criteria regarding the performance of preoperative chest computed tomography (CT) in patients with cT1a renal cell carcinoma (RCC) exists. We aimed to establish an objective standard for the optimal timing of preoperative chest CT in patients with RCC. Data from 890 patients who underwent surgical treatment for RCC between January 2011 and December 2020 were retrospectively collected. The primary endpoint was detection of lung metastasis on chest CT before nephrectomy. A multivariable logistic regression model predicting positive chest CT scans was used. Predictors included preoperative cTN stage, presence of systemic symptoms, Charlson comorbidity index (CCI), platelet count/hemoglobin ratio, albumin/globulin ratio (AGR), and De Ritis ratio. The overall rate of positive chest CT scans before nephrectomy was 3.03% (27/890). Only one patient had lung metastasis before surgery for cT1a. cT stage (≥cT1b), CCI ≥4, and low AGR were associated with a higher risk of positive chest CT scans. The best cutoff value for AGR was 1.39. After 890-sample bootstrap validation, the concordance index was 0.80. The net benefit of the proposed strategy was superior to that of the select-all and select-none strategies according to decision curve analysis. Therefore, when chest CT scans were performed with a risk of a positive result ≥10%, 532 (59.8%) negative chest CT scans could be prevented. Only 24 (2.7%) potentially positive chest CT scans were misdiagnosed. Therefore, we recommend chest CT in patients with ≥cT1b disease, CCI ≥4, and low AGR.
A lower bound for the k ‐multicolored sum‐free problem in Zmn

In this paper, we give a lower bound for the maximum size of a k ‐colored sum‐free set in Zmn , where k⩾3 and m⩾2 are fixed and n tends to infinity. If m is a prime power, this lower bound matches (up to lower order terms) the previously known upper bound for the maximum size of a k ‐colored sum‐free set in Zmn . This generalizes a result of Kleinberg–Sawin–Speyer for the case k=3 and as part of our proof we also generalize a result by Pebody that was used in the work of Kleinberg–Sawin–Speyer. Both of these generalizations require several key new ideas.
The Kirchhoff Index of Enhanced Hypercubes

Let $\{e_{1},\ldots,e_{n}\}$ be the standard basis of abelian group $Z_{2}^{n}$, which can be also viewed as a linear space of dimension $n$ over the Galois filed $F_{2}$, and $\epsilon_{k}=e_k+e_{k+1}+\cdots+e_n$ for some $1\le k\le n-1$. It is well known that the so called enhanced hypercube $Q_{n, k}(1\le k \le n-1)$ is just the Cayley graph $Cay(Z_{2}^{n},S)$ where $S=\{e_{1},\ldots, e_{n},\epsilon_{k}\}$. In this paper, we obtain the spectrum of $Q_{n, k}$, from which we give an exact formula of the Kirchhoff index of the enhanced hypercube $Q_{n, k}$. Furthermore, we prove that, for a given $n$, $Kf(Q_{n, k})$ is increased with the increase of $k$. Finally, we get $\lim\limits_{n\to\infty}\frac{Kf(Q_{n, k})}{\frac{2^{2n}}{n+1}}=1$.
On a two-phase Serrin-type problem and its numerical computation

We consider an overdetermined problem of Serrin-type with respect to an operator in divergence form with piecewise constant coefficients. We give sufficient condition for unique solvability near radially symmetric configurations by means of a perturbation argument relying on shape derivatives and the implicit function theorem. This problem is also treated numerically, by means of a steepest descent algorithm based on a Kohn–Vogelius functional.
Phase-field systems for grain boundary motions under isothermal solidifications

Two main existence theorems are proved for two nonstandard systems of parabolic initial-boundary value problems. The systems are based on the "$ \phi $-$ \eta $-$ \theta $ model" proposed by Kobayashi [RIMS Kokyuroku, 1210 (2001), 68-77] as a phase-field model of planar grain boundary motion under isothermal solidification. Although each of the systems has specific characteristics and mathematical difficulties, the proofs of the main theorems are based on the time discretization method by means of a common approximating problem. As a consequence, we provide a uniform solution method for a wide scope of parabolic systems associated with the $ \phi $-$ \eta $-$ \theta $ model.
Topological quasi-group shifts

In this work we characterize those shift spaces which can support a 1-block quasi-group operation and show the analogous of Kitchens result: any such shift is conjugated to a product of a full shift with a finite shift. Moreover, we prove that every expansive automorphism on a compact zero-dimensional quasi-group that verifies the medial property, commutativity and has period 2, is isomorphic to the shift map on a product of a finite quasi-group with a full shift.
Hadronic unquenching effects in the quark propagator

We investigate hadronic unquenching effects in light quarks and mesons. Within the nonperturbative continuum framework of Schwinger-Dyson and Bethe-Salpeter equations we quantify the strength of the back reaction of the pion onto the quark-gluon interaction. To this end we add a Yang-Mills part of the interaction such that unquenched lattice results for various current quark masses are reproduced. We find considerable effects in the quark mass function at low momenta as well as for the chiral condensate. The quark wave function is less affected. The Gell-Mann-Oakes-Renner relation is valid to good accuracy up to pion masses of 400-500 MeV. As a by-product of our investigation we verify the Coleman theorem, that chiral symmetry cannot be broken spontaneously when QCD is reduced to 1+1 dimensions.
Bacterial Magnetosomes Release Iron Ions and Induce Regulation of Iron Homeostasis in Endothelial Cells

Magnetosomes (MAGs) extracted from magnetotactic bacteria are well-defined membrane-enveloped single-domain magnetic nanoparticles. Due to their superior magnetic and structural properties, MAGs constitute potential materials that can be manipulated via genetic and chemical engineering for use in biomedical and biotechnological applications. However, the long-term effects exerted by MAGs on cells are of concern in the context of in vivo applications. Meanwhile, it remains relatively unclear which mechanisms are employed by cells to process and degrade MAGs. Hence, a better understanding of MAGs’ degradation and fundamental signal modulations occurring throughout this process is essential. In the current study, we investigated the potential actions of MAGs on endothelial cells over a 10-day period. MAGs were retained in cells and found to gradually gather in the lysosome-like vesicles. Meanwhile, iron-ion release was observed. Proteomics further revealed a potential cellular mechanism underlying MAGs degradation, in which a group of proteins associated with vesicle biogenesis, and lysosomal enzymes, which participate in protein hydrolysis and lipid degradation, were rapidly upregulated. Moreover, the released iron triggered the regulation of the iron metabolic profiles. However, given that the levels of cell oxidative damage were relatively stable, the released iron ions were handled by iron metabolic profiles and incorporated into normal metabolic routes. These results provide insights into the cell response to MAGs degradation that may improve their in vivo applications.
Effects of Genotype and Diet on Performance, Carcass Traits, and Blood Profiles of Slow-Growing Chicks Obtained by Crosses of Local Breed with Commercial Genotype

The effects of genotype and diet on growth performance, carcass traits and blood metabolites were investigated. The commercial Ross 308 (R) chickens genotype, a local Black Transylvanian Naked Neck (BTNN) breed, and their crosses were used in an 81-day study. A total of 720 one-d-old chicks were allotted into eight groups in a 4 × 2 factorial design with 4 genotypes: Rmale × Rfemale (R), BTNNmale × Rfemale (BTNN-R), BTNNmale × BTNNfemale (BTNN), Rmale × BTNNfemale (R-BTNN), and 2 diets: control and low-metabolisable energy (LME). Genotype affected performance parameters, namely body weight gain (BWG), feed intake (FI), energy intake (EI), feed conversion ratio (FCR), energy conversion ratio (ECR), and production efficiency factor (PEF), irrespective of growth phase (p < 0.05). Diet had no significant effect on overall BWG, EI, ECR and PEF, except that it increased FI and FCR. Genotype influenced the carcass and organ yields (p < 0.05), except bursa weight, while diet had no significant effect. Blood parameters (total cholesterol, triglycerides, glucose, albumin and phosphorus) were affected only by genotype (p < 0.05). In summary, results show that from the two crossbreedings obtained between R and BTNN genotypes, the BTNN-R growth performance and carcass traits were superior to R-BTNN, even though both have had a similar improved plasma response. Lowering the ME level did not significantly affect the BWG but increased FI and FCR, whereas the production index was similar regardless of the genotype. Based on the present results, we concluded that the BTNN-R crosses are the most suitable for use in alternative rearing systems for slow-growing chickens.
Acute Effects of Neuromuscular Electrical Stimulation on Contralateral Plantar Flexor Neuromuscular Function

Simple Summary The increase in maximal voluntary strength of one limb (e.g., right leg) while transcutaneous neuromuscular electrical stimulation is concomitantly applied to the contralateral limb (e.g., left leg) has been termed contralateral facilitation. This effect has previously been reported for the knee extensors but the underlying mechanisms are still unclear. It is also not known whether or not other muscle groups may show contralateral facilitation. Here we investigated the effect of two electrical stimulation modalities, which were compared to a submaximal voluntary contraction (~10% maximal voluntary strength) and a resting condition, on contralateral facilitation of the calf muscles. Maximal voluntary strength, and various neural parameters derived from strength and surface electromyography measurements were quantified for each condition. Our results showed that neither voluntary contraction nor electrical stimulation of the ipsilateral plantar flexors induced a contralateral facilitation of the calf muscles. This absence contrasts with the results obtained on the knee extensors and can be attributed to the absence of neural changes observed on the contralateral side. These findings should be considered by clinicians/researchers in lower-limb rehabilitation settings, as it seems easier to induce contralateral facilitation in proximal vs. distal lower limbs. Abstract Contralateral facilitation, i.e., the increase in contralateral maximal voluntary strength that is observed when neuromuscular electrical stimulation (NMES) is applied to the ipsilateral homonymous muscle, has previously been reported for the knee extensors but the neurophysiological mechanisms remain to be investigated. The aim of this study was to compare plantar flexor contralateral facilitation between a submaximal voluntary contraction (~10% MVC torque) and two evoked contractions (conventional and wide-pulse high-frequency NMES) of the ipsilateral plantar flexors, with respect to a resting condition. Contralateral MVC torque and voluntary activation level were measured in 22 healthy participants while the ipsilateral plantar flexors were at rest, voluntarily contracted or stimulated for 15 s. Additional neurophysiological parameters (soleus H-reflex and V-wave amplitude and tibialis anterior coactivation level) were quantified in a subgroup of 12 participants. Conventional and wide-pulse high-frequency NMES of the ipsilateral plantar flexors did not induce any contralateral facilitation of maximal voluntary strength and activation with respect to the resting condition. Similarly, no alteration of neurophysiological parameters was observed in the different conditions. This absence of contralateral facilitation contrasts with some results previously obtained on the knee extensors but is consistent with the absence of neurophysiological changes on the contralateral soleus.
The Spectral Side of Stable Local Trace Formula

Let $G$ be a connected quasi-split reductive group over $\mathbb{R}$, and more generally, a quasi-split $K$-group over $\mathbb{R}$. Arthur had obtained the formal formula for the spectral side of the stable local trace formula, by using formal substitute of Langlands parameters. In this paper, we construct the spectral side of the stable trace formula and endoscopy trace formula directly for quasi-split $K$-groups over $\mathbb{R}$, by incorporating the works of Shelstad. In particular we give the explicit expression for the spectral side of the stable local trace formula, in terms of Langlands parameters.
Additive twists of Fourier coefficients of GL(3) Maass forms

Substantial work has been done in studying sums involving coefficients attached to various L-functions. A very classical example is the problem of estimating exponential sums of the form ∑ n≤x n , which is related to subconvex bounds for the Riemann zeta function and to Dirichlet’s divisor problem. For more on this, see, for instance, Chapters V and XII in [14]. A vast literature also exists for the estimation of character sums. These are, among other things, related to subconvexity for Dirichlet L-functions and estimates for the least quadratic non-residue. See, for instance, Chapter 12 of [8]. The estimation of sums of coefficients twisted by additive characters is also classical. To be specific, we shall be interested in sums of the type S = ∑
Reconstruction of piecewise constant signals by minimization of the $L^1$-Potts functional

We recover piecewise constant signals from noisy measurements $f$ by the minimization of the $L^1$-Potts functional $\gamma |\nabla u|_0$ + $|u - f|_1. $ We present an $O(n^2)$ time and O(n) space algorithm for the computation of an exact minimizer of this non-convex optimization problem. We show that our algorithm recovers mildly blurred piecewise constant signals without knowledge of the blurring operator. For stronger blurred signals and known blurring operator, we derive an iterative reconstruction algorithm.