Miracle-dz/UniFAR-FTUs huggingface dataset:
Improved effective estimates of P\'olya's Theorem for quadratic forms

Following de Loera and Santos, the P\'olya exponent of a $n$-ary real form (i.e. a homogeneous polynomial in $n$ variables with real coefficients) $f$ is the infimum of the upward closed set of nonnegative integers $m$ such that $(x_1 + \cdots + x_n)^m f$ strictly has positive coefficients. By a theorem of P\'olya, a form assumes only positive values over the standard $(n - 1)$-simplex in Euclidean $n$-space if and only if its P\'olya exponent is finite. In this note, we compute an upper bound of the P\'olya exponent of a quadratic form $f$ that assumes only positive values over the standard simplex. Our bound improves a previous upper bound due to de Klerk, Laurent and Parrilo. For example, for the binary quadratic form $f_\kappa = \lambda^2 x_1^2 - 2 \kappa \lambda x_1 x_2 + x_2^2$, which assumes only positive values over the standard $1$-simplex whenever $0 \le \kappa < 1 < \lambda$, our upper bound of its P\'olya's exponent is $O(1/\lambda)$ times that of de Klerk, Laurent and Parrilo's as $\lambda$ tends to infinity.
DuBox: No-Prior Box Objection Detection via Residual Dual Scale Detectors

Traditional neural objection detection methods use multi-scale features that allow multiple detectors to perform detecting tasks independently and in parallel. At the same time, with the handling of the prior box, the algorithm's ability to deal with scale invariance is enhanced. However, too many prior boxes and independent detectors will increase the computational redundancy of the detection algorithm. In this study, we introduce Dubox, a new one-stage approach that detects the objects without prior box. Working with multi-scale features, the designed dual scale residual unit makes dual scale detectors no longer run independently. The second scale detector learns the residual of the first. Dubox has enhanced the capacity of heuristic-guided that can further enable the first scale detector to maximize the detection of small targets and the second to detect objects that cannot be identified by the first one. Besides, for each scale detector, with the new classification-regression progressive strapped loss makes our process not based on prior boxes. Integrating these strategies, our detection algorithm has achieved excellent performance in terms of speed and accuracy. Extensive experiments on the VOC, COCO object detection benchmark have confirmed the effectiveness of this algorithm.
Clinical Delays and Comparative Outcomes in Younger and Older Adults with Colorectal Cancer: A Systematic Review

Outcome disparities between adults <50 with colorectal cancer (CRC) and older adults may be explained by clinical delays. This study synthesized the literature comparing delays and outcomes between younger and older adults with CRC. Databases were searched until December 2021. We included studies published after 1990 reporting delay in adults <50 that made comparisons to older adults. Comparisons were described narratively and stage between age groups was meta-analyzed. 39 studies were included representing 185,710 younger CRC patients and 1,422,062 older patients. Sixteen delay intervals were compared. Fourteen studies (36%) found significantly longer delays among younger adults, and nine (23%) found shorter delays among younger patients. Twelve studies compared time from symptom onset to diagnosis (N younger = 1538). Five showed significantly longer delays for younger adults. Adults <50 years also had higher odds of advanced stage (16 studies, pooled OR for Stage III/IV 1.76, 95% CI 1.52–2.03). Ten studies compared time from diagnosis to treatment (N younger = 171,726) with 4 showing significantly shorter delays for younger adults. All studies showing longer delays for younger adults examined pre-diagnostic intervals. Three studies compared the impact of delay on younger versus older adult. One showed longer delays were associated with advanced stage and worse survival in younger but not older adults. Longer delays among younger adults with CRC occur in pre-diagnostic intervals.
Reduced Order Modeling for Nonlinear PDE-constrained Optimization using Neural Networks

Nonlinear model predictive control (NMPC) often requires real-time solution to optimization problems. However, in cases where the mathematical model is of high dimension in the solution space, e.g. for solution of partial differential equations (PDEs), black-box optimizers are rarely sufficient to get the required online computational speed. In such cases one must resort to customized solvers. This paper present a new solver for nonlinear time-dependent PDE-constrained optimization problems. It is composed of a sequential quadratic programming (SQP) scheme to solve the PDE-constrained problem in an offline phase, a proper orthogonal decomposition (POD) approach to identify a lower dimensional solution space, and a neural network (NN) for fast online evaluations. The proposed method is showcased on a regularized least-square optimal control problem for the viscous Burgers’ equation. It is concluded that significant online speed-up is achieved, compared to conventional methods using SQP and finite elements, at a cost of a prolonged offline phase and reduced accuracy.
Characterizing Elastic Turbulence in Channel Flows at Low Reynolds number

We experimentally investigate the flow of a viscoelastic fluid in a parallel shear geometry at low Reynolds number. As the flow becomes unstable via a nonlinear subcritical instability, velocimetry measurements show non-periodic fluctuations over a broad range of frequencies and wavelengths, consistent with the main features of elastic turbulence. Using the same experimental setup, we compare these features to those in the flow around cylinders, which is upstream to the parallel shear region; we find significant differences in power spectra scaling, intermittency statistics, and flow structures. We propose a simple mechanism to explain the growth of velocity fluctuations in parallel shear flows based on polymer stretching due to fluctuations in streamwise velocity gradients.
Probabilistic approach to the quantum separation effect for the Feynman–Kac semigroup

Quantum tunnelling phenomenon allows a particle in Schr\"odinger mechanics tunnels through a barrier that it classically could not overcome. Even the infinite potentials do not always form impenetrable barriers. We discuss an answer to the following question: What is a critical magnitude of potential, which creates impenetrable barrier and for which the corresponding Schr\"odinger evolution system separates? In addition we describe some quantitative estimates for the separating effect in terms of cut-off potentials.
Generalized Kubo formulas for the transport properties of incommensurate 2D atomic heterostructures

We give an exact formulation for the transport coefficients of incommensurate two-dimensional atomic multilayer systems in the tight-binding approximation. This formulation is based upon the C* algebra framework introduced by Bellissard and collaborators [Coherent and Dissipative Transport in Aperiodic Solids, Lecture Notes in Physics (Springer, 2003), Vol. 597, pp. 413–486 and J. Math. Phys. 35(10), 5373–5451 (1994)] to study aperiodic solids (disordered crystals, quasicrystals, and amorphous materials), notably in the presence of magnetic fields (quantum Hall effect). We also present numerical approximations and test our methods on a one-dimensional incommensurate bilayer system.
Blow-up analysis for nodal radial solutions in Moser-Trudinger critical equations in R^2

In this paper we consider nodal radial solutions $u_\epsilon$ to the problem \[ \begin{cases} -\Delta u=\lambda ue^{u^2+|u|^{1+\epsilon}}&\text{ in }B,\\ u=0&\text{ on }\partial B. \end{cases} \] and we study their asymptotic behaviour as $\epsilon\searrow0$, $\epsilon>0$. We show that when $u_\epsilon$ has $k$ interior zeros, it exhibits a multiple blow-up behaviour in the first $k$ nodal sets while it converges to the least energy solution of the problem with $\epsilon=0$ in the $(k+1)$-th one. We also prove that in each concentration set, with an appropriate scaling, $u_\epsilon$ converges to the solution of the classical Liouville problem in $R^2$.
Proposal of a New Rating Concept for Digital Health Applications in Orthopedics and Traumatology

Background: Health-related mobile applications (apps) are rapidly increasing in number. There is an urgent need for assessment tools and algorithms that allow the usability and content criteria of these applications to be objectively assessed. The aim of this work was to establish and validate a concept for orthopedic societies to rate health apps to set a quality standard for their safe use. Methods: An objective rating concept was created, consisting of nine quality criteria. A self-declaration sheet for app manufacturers was designed. Manufacturers completed the self-declaration, and the app was examined by independent internal reviewers. The pilot validation and analysis were performed on two independent health applications. An algorithm for orthopedic societies was created based on the experiences in this study flow. Results: “Sprunggelenks-App“ was approved by the reviewers with 45 (98%) fulfilled criteria and one (2%) unfulfilled criterion. “Therapie-App” was approved, with 28 (61%) met criteria, 6 (13%) unfulfilled criteria and 12 (26%) criteria that could not be assessed. The self-declaration completed by the app manufacturer is recommended, followed by a legal and technical rating performed by an external institution. When rated positive, the societies’ internal review using independent raters can be performed. In case of a positive rating, a visual certification can be granted to the manufacturer for a certain time frame. Conclusion: An objective rating algorithm is proposed for the assessment of digital health applications. This can help societies to improve the quality assessment, quality assurance and patient safety of those apps. The proposed concept must be further validated for inter-rater consistency and reliability.
Clock statistics for 1d Schrödinger operators

We study the 1d Schrödinger operators with alloy type random supercritical decaying potential, where the random variables {ω(j)}j∈Z in the potential are either i.i. d. or more generally ones with exponentially decaying correlations. We prove the convergence to the clock process for the local statistics of eigenvalues. Moreover we prove the strong clock behavior in i.i. d. case.
Toward a Combination of Biomarkers for Molecular Characterization of Multiple Sclerosis

Multiple sclerosis (MS) is an autoimmune disease affecting the central nervous system associated with chronic inflammation, demyelination, and axonal damage. MS is a highly heterogeneous disease that leads to discrepancies regarding the clinical appearance, progression, and therapy response of patients. Therefore, there is a strong unmet need for clinically relevant biomarkers capable of recapitulating the features of the disease. Experimental autoimmune encephalomyelitis (EAE) is a valuable model for studying the pathophysiology of MS as it recapitulates the main hallmarks of the disease: inflammation, blood-brain barrier (BBB) disruption, gliosis, myelin damage, and repair mechanisms. In this study, we used the EAE-PLP animal model and established a molecular RNA signature for each phase of the disease (onset, peak, remission). We compared variances of expression of known biomarkers by RT-qPCR in the brain and spinal cord of sham and EAE animals monitoring each of the five hallmarks of the disease. Using magnetic cell isolation technology, we isolated microglia and oligodendrocytes of mice of each category, and we compared the RNA expression variations. We identify genes deregulated during a restricted time frame, and we provide insight into the timing and interrelationships of pathological disease processes at the organ and cell levels.
Boundary exponential stabilization of 1-D inhomogeneous quasilinear hyperbolic systems

This paper deals with the problem of boundary stabilization of first-order n\times n inhomogeneous quasilinear hyperbolic systems. A backstepping method is developed. The main result supplements the previous works on how to design multi-boundary feedback controllers to realize exponential stability of the original nonlinear system in the spatial H^2 sense.
Generalized chord diagram expansions of Dyson–Schwinger equations

Series solutions for a large family of single equation Dyson-Schwinger equations are given as expansions over decorated rooted connected chord diagrams. The analytic input to the new expansions are the expansions of the regularized integrals for the primitive graphs building the Dyson-Schwinger equation. Each decorated chord diagram contributes a weighted monomial in the coefficients of the expansions of the primitives and so indexes the analytic solution in a tightly controlled way.
Implementing Multiple Imputation for Missing Data in Longitudinal Studies When Models are Not Feasible: An Example Using the Random Hot Deck Approach

Purpose Researchers often use model-based multiple imputation to handle missing at random data to minimize bias. However, constraints within the data may sometimes result in implausible values, making model-based imputation infeasible. In these contexts, we illustrate how random hot deck imputation can allow for plausible multiple imputation in longitudinal studies. Patients and Methods Our motivating example is the Childhood Health, Activity, and Motor Performance School Study Denmark (CHAMPS-DK), a prospective cohort study that measured weekly sports participation for 1700 Danish schoolchildren. Using observed data on 4 variables (pain, activity frequency, sport, sport counts), we created a gold-standard data set without missing data. We then created a synthetic data set by setting some variable values to missing based on a prediction model that mimicked real-data missingness patterns. To create 5 imputed data sets, we matched each record with missing data to several fully observed records, generated probabilities from matched records, and sampled from these records based on the probability of each occurring. We assessed variability and agreement (kappa) between the imputed data sets and the gold-standard data set. We compare results to common model-based imputation methods. Results Variability across data sets appeared reasonable. The range of kappa for the random hot deck approach was moderate for activity frequency (0.65 to 0.71) and sport (0.59 to 0.85), and poor for common model-based approaches (range 0.00 to 0.11). The range of kappas for sport count was strong (0.87 to 0.97) for random hot deck imputation and weak to moderate (0.55 to 0.71) for common model-based imputation. Agreement was higher when more information was present, and when prevalence was higher for our binary variable sport. Conclusion Random hot deck imputation should be considered as an alternative method when model-based approaches are infeasible, specifically where there are constraints within and between covariates.
Non-Gaussian fluctuations of randomly trapped random walks

Abstract In this paper we consider the one-dimensional, biased, randomly trapped random walk with infinite-variance trapping times. We prove sufficient conditions for the suitably scaled walk to converge to a transformation of a stable Lévy process. As our main motivation, we apply subsequential versions of our results to biased walks on subcritical Galton–Watson trees conditioned to survive. This confirms the correct order of the fluctuations of the walk around its speed for values of the bias that yield a non-Gaussian regime.
Constant scalar curvature Kähler metrics on rational surfaces

We consider projective rational strong Calabi dream surfaces: projective smooth rational surfaces which admit a constant scalar curvature Kähler metric for every Kähler class. We show that there are only two such rational surfaces, namely the projective plane and the quadric surface. In particular, we show that all rational surfaces other than those two admit a destabilising slope test configuration for some polarisation, as introduced by Ross and Thomas. We further show that all Hirzebruch surfaces other than the quadric surface and all rational surfaces with Picard rank 3 do not admit a constant scalar curvature Kähler metric in any Kähler class.
Risk Sensitive Multiple Goal Stochastic Optimization, with application to Risk Sensitive Partially Observed Markov Decision Processes

We study Risk Sensitive Partially Observable Markov Decision Processes (RSPOMDPs) where the performance index is either the expected utility corresponding to a function that can be written as a weighed sum of exponentials or the expected shortfall generated by functions of the hyperbolic sine type. In that direction we utilize methods for treating Risk Sensitive Multiple Goal Markov Decision Processes (RSMGMDPs) where the performance index is given by sums of expected utilities, where each utility is applied to a different running cost, but also methods from the theory of Risk Sensitive Constrained Markov Decision Processes (RSCMDPs).
Local Employment in Tourist Attraction: A Community Perspective

Participation of local communities is a criterion that is often agreed upon as an important condition for the development and sustainability of all forms of tourism. Local employment becomes one form of recruitment that tourist attractions often carry out. However, increasing local participation in tourism often creates friction between tourist attractions and residents. This research aims to explore local participation in The Lodge Maribaya, one of the popular tourist attractions in Bandung West Java, by investigating factors influencing the community's support for local employment in the area. Data was collected using a structured questionnaire from 59 employees who are locals in the area. The confirmatory factor analysis was utilized to test the construct validity and reliability of the model. At the same time, Partial Least Squares (PLS) modeling was employed to assess the relationship among the variables. This study has found that community attachment and perceived benefits play an important role in the community's support in The Lodge Maribaya in terms of their participation in local employment. The strong community attachments and the considerable benefits perceived by the community are cogitated to be the main factors in The Lodge Maribaya's success in employing local workers. By investigating this perspective, this study is expected to provide insights on how to increase local participation in employment and anticipate the aspect that may hinder the process
A time-splitting finite-element approximation for the Ericksen-Leslie equations

In this paper we propose a time-splitting finite-element scheme for approximating solutions of the Ericksen-Leslie equations governing the flow of nematic liquid crystals. These equations are to be solved for a velocity vector field and a scalar pressure as well as a director vector field representing the direction along which the molecules of the liquid crystal are oriented. The algorithm is designed at two levels. First, at the variational level, the velocity, pressure and director are computed separately, but the director field has to be computed together with an auxiliary variable in order to deduce a priori energy estimates. Second, at the algebraic level, one can avoid computing such an auxiliary variable if this is approximated by a piecewise constant finite-element space. Therefore, these two steps give rise to a numerical algorithm that computes separately only the primary variables. Moreover, we will use a pressure stabilization technique that allows an stable equal-order interpolation for the velocity and the pressure. Finally, some numerical simulations are performed in order to show the robustness and efficiency of the proposed numerical scheme and its accuracy.
Stieltjes Integral Theorem and The Hilbert Transform

Stieltjes integral theorem is more commonly known by the phrase 'integration by parts' and enables rearrangement of an otherwise intractable integral to a more amenable form; often permitting completion of an integral in closed form. Applying Stieltjes integral theorem to the Hilbert transform yields an equivalent alternate integral definition, which is homeomorphic and exhibits accelerated computation. By virtue of the convolution theorem, the integral is mapped to Fourier image space and delineates requirements for the inverse Fourier transform, also, these requirements reveal the underlying reason for increased computational speed. Lastly, an alternative to Cauchy's integral formula is deduced by extending the line integral into the complex domain and involves a line integral with logarithmic kernel.
On the existence of ratio limits of weighted $n$-generalized Fibonacci sequences with arbitrary initial conditions

We study ratio limits of the consecutive terms of weighted $n$-generalized Fibonacci sequences generated from arbitrary complex initial conditions by linear recurrences with arbitrary complex weights. We prove that if the characteristic polynomial of such a linear recurrence is asymptotically simple, then the ratio limit exists for any sequence generated from arbitrary nontrivial initial conditions and it is equal to the unique zero of the characteristic polynomial.
Spectral geometries on a compact metric space

The notion of a spectral geometry on a compact metric space X is introduced. This notion serves as a discrete approximation of X motivated by the notion of a spectral triple from non-commutative geometry. A set of axioms charaterising spectral geometries is given. Bounded deformations of spectral geometries are studied and the relationship between the dimension of a spectral geometry and more traditional dimensions of metric spaces is investigated.